A classic trope of hard sci-fi as well as more serious futurism is using self-replicating nanoassemblers to convert planets of the Solar System to computronium, or some other kind of a Dyson swarm. This is almost the default way to colonize space in any projection of the future that features singularity or ASI, and not uncommon in other settings as well.
Except that even if we grant the nano part works exactly as advertised, and even if we ignore the gas giants and only focus on rocky and icy bodies that have a hard surface - which constitute less than 1% of the total planetary mass, by the way - there are at least two very fundamental problems, each one making it basically impossible to use self-replicating nanobots as the primary tool for space colonization: matter and energy. I'll go over each one in turn.
(Caveat: this post is specifically about using nanoassemblers to colonize space on planetary scale. There are a lot of arguments for why they can or can not work conceptually, and whether a runaway grey goo scenario is likely within the Earth biosphere. I don't have the expertise in any of the relevant fields to contribute to those discussions. Instead I'm presenting a weaker claim: even if nanoassemblers can be made to work on the nanoscale, they aren't suitable as a planet-shaping tool. I think this claim can be supported just by the basic physics and chemistry.)
Matter
Suppose you have a perfectly functional self-replicating nanobot design that can convert raw input materials into more of itself, or any other output you desire. You've solved "fat fingers" and "sticky fingers" and ironed out all the other issues. As any other machine - or biological cell - it is composed of more or less fixed list of elements in more or less specific proportions. There may be some wiggle room - a cell can tolerate some variation in ion levels, a machine can substitute some steel parts for bronze or aluminum - but the variation is very much limited. Different chemical elements have very different properties and can't be swapped out for each other freely.
The problem is, compositions of celestial bodies vary wildly. At the most global scale, inner rocky planets consist mostly of iron, oxygen, silicon, and magnesium by mass, and only have carbon, hydrogen and nitrogen at a small fraction of a percent (Earth has a relative abundance of C,H,N on the surface, but not overall). Icy moons of the outer planets, on the other hand, have nothing but those three elements plus oxygen for tens or hundreds of kilometers deep, before you reach the rocky core. Is your nanobot design so flexible that you can make it from both sets of inputs, with just one element in common?[1] And you do have to make it from those inputs if you are talking about converting the entire planet. You can't just say "it will refine the trace elements available" - this just results in trace amounts of nanobots on the surface of an otherwise largely unchanged planet.
But can't you just send different designs to different planets? That doesn't help either, even if we assume it is possible to build nanobots from all of those different sets of elements - and that's one hell of an assumption. Because then you just run into the same issue on a smaller scale - you'll have your Mars Pattern Nanobot, perfectly tuned to reflect the average composition of Mars (which includes 36% iron, 9% magnesium), sitting in the middle of a many kilometers-wide plain of nearly pure SiO4, and its sibling somewhere near the pole, surrounded mostly by H2O, neither quite sure what to do next.
Of course within one planet we can have nanobots shipping materials around. But to accomplish that, the they would likely need to combine into some sort of macro-scale agglomerates - for speed, energy efficiency and to easier overcome obstacles. They would probably also need to build or assemble some kind of clear passageways for the same reasons. And since so much of the input materials would need to be shipped in, it would only make sense to process it all in one place rather then re-distribute it evenly across a thin film of nanobots. But by that point if we have roads, trucks and factories, why exactly are we bothering with the "nano" part?
Alternatively, the problem can be solved if the nanobots can also do nuclear transmutation, converting elements into each other. But right now this is an absurdly inefficient process requiring giant particle accelerators, and to the best of my knowledge nobody has even a slightest idea of how (or if) it may be accomplished on the nano-scale and with a reasonable energy efficiency. Which brings us to the next problem.
Energy
In addition to raw inputs, nanobots need some energy to tear apart those constituent elements, assemble them into new nanobots or other useful stuff, and, since we're talking about converting the planets into a Dyson swarm or Matrioshka brain, also to launch the outputs into orbit. Each of these steps requires energy. Lets go over all possible energy sources.
Chemical - this is straight out because we are largely disassembling rock, and rock is at or near its thermodynamic floor. So is water which is the main component of crust of the outer moons. In fact, we will be spending a lot of energy just to tear those elements apart.
Nuclear fission - possible in principle, but it turns the element abundancy problem into an even bigger show stopper than before. Most places just don't have any meaningful amount of fissile fuel.
Nuclear fusion - one of the main difficulties with doing it on the macro scale is that the reactors we build are not big enough - and the reactors we build are the size of a building. Making it work on the nano-scale would be some magic-level technology indeed. And it also aggravates the material problem, though not to the same extent as fission, because deuterium is rare even on the bodies that do have water.
Solar - this is the only viable option with the technologies we can at least hypothesize as possible. Viable in the sense that we can be reasonably sure nanobots across all of the solar system can at least get some energy this way. Lets look at it a bit closer.
The very best place in the solar system to do solar-powered planet disassembly is the day side of Mercury. To further simplify the task, I'll only consider the energy cost of breaking down the rock into its constituent elements. I will ignore the cost of assembling them into a new configuration, as well as the cost of lifting the outputs into the Mercury's orbit. I'll also assume 100% efficiency for all the processes involved, from solar power collection to reducing the minerals.
The relevant numbers are: average solar flux at Mercury's orbit is 9000 W/m², chemical binding energy of rock is ~10 MJ/kg, and rock density is around 3000 kg/m³. ⁶ seconds or 38 days for the nanobots to "eat" through 1 meter of rock. On the day side. At the equator. Averaged over the whole planet it's 4 times slower, so our hypothetical gray goo swarm is eating away at Mercury at the terrifyingly fast pace of 2.4 meters per year. Mercury's radius is, conveniently, about 2400 km, so it will take just about one million years to convert all of Mercury into something more useful. Still fairly fast by astronomical standards, but infinitely long by civilizational timescales. It does turn into multiple millions if we account for all the costs we've ignored in our model, and goes into eight digits as we move out to Venus which is both a lot bigger and receives less sunlight per unit surface[2].
To speed things up, we could build giant mirrors in orbit to focus solar energy on the planet, or better yet solar power arrays and emitters, converting it to some uniform wavelength which can be collected by our nanobots more efficiently. We'd need to have flight trajectories for whichever launch method we use clear of this massive flux of energy. And in any realistic scenario, we also need very large and very hot radiators to re-emit the waste heat. So the whole picture, again, begins to look less like a homogeneous and autonomous grey goo and more like a mega-scale logistics web with nanoassemblers being one node in it.
Conclusion
I'm not saying that nanoassemblers won't be an extremely useful tool in space colonization - obviously they will be. Being able to assemble anything from the raw materials using the same instrument, an instrument that can be scaled up or down smoothly and indefinitely, is a wildly beneficial capability to have in any situation, but in particular when colonizing extremely remote environments where nearly every task requires advanced technology.
And of course it is possible that a god-level ASI can invent nano-scale nuclear fusion and transmutation, or maybe even it can tell conservation laws to bugger off entirely. If you postulate this kind of power, forecasting is useless and worldbuilding is only limited by your imagination.
But within the limits of known or at least vaguely hypothesized physics, nanoassemblers will be just one tool in a toolbox, not a magic pill that you can drop on a planet, wait for a few years/decades, and come back to a planet mass worth of goodies. Even with this technology, seriously colonizing Solar System will require planetary and inter-planetary scale logistics in both matter and energy, and things like constructing a Dyson swarm would take at least multiple centuries, and more likely many, many millennia.
As mentioned, I'm making the task easier for nanobots by not considering the giant planets, even though they are 99% of the planetary mass. If we include them, it gets beyond hopeless since they are mostly hydrogen and helium - good luck making complex molecules out of those.
Speaking of surface: how do nanobots survive and how all those delicate large molecules continue to function at the Venus surface, with the temperatures higher than that of boiling oil? I've no idea. There is very little sunlight there anyway thanks to the thick atmosphere. Maybe you can get clever with nanobots floating in the upper atmosphere using oxygen as the lifting gas.
A classic trope of hard sci-fi as well as more serious futurism is using self-replicating nanoassemblers to convert planets of the Solar System to computronium, or some other kind of a Dyson swarm. This is almost the default way to colonize space in any projection of the future that features singularity or ASI, and not uncommon in other settings as well.
Except that even if we grant the nano part works exactly as advertised, and even if we ignore the gas giants and only focus on rocky and icy bodies that have a hard surface - which constitute less than 1% of the total planetary mass, by the way - there are at least two very fundamental problems, each one making it basically impossible to use self-replicating nanobots as the primary tool for space colonization: matter and energy. I'll go over each one in turn.
(Caveat: this post is specifically about using nanoassemblers to colonize space on planetary scale. There are a lot of arguments for why they can or can not work conceptually, and whether a runaway grey goo scenario is likely within the Earth biosphere. I don't have the expertise in any of the relevant fields to contribute to those discussions. Instead I'm presenting a weaker claim: even if nanoassemblers can be made to work on the nanoscale, they aren't suitable as a planet-shaping tool. I think this claim can be supported just by the basic physics and chemistry.)
Matter
Suppose you have a perfectly functional self-replicating nanobot design that can convert raw input materials into more of itself, or any other output you desire. You've solved "fat fingers" and "sticky fingers" and ironed out all the other issues. As any other machine - or biological cell - it is composed of more or less fixed list of elements in more or less specific proportions. There may be some wiggle room - a cell can tolerate some variation in ion levels, a machine can substitute some steel parts for bronze or aluminum - but the variation is very much limited. Different chemical elements have very different properties and can't be swapped out for each other freely.
The problem is, compositions of celestial bodies vary wildly. At the most global scale, inner rocky planets consist mostly of iron, oxygen, silicon, and magnesium by mass, and only have carbon, hydrogen and nitrogen at a small fraction of a percent (Earth has a relative abundance of C,H,N on the surface, but not overall). Icy moons of the outer planets, on the other hand, have nothing but those three elements plus oxygen for tens or hundreds of kilometers deep, before you reach the rocky core. Is your nanobot design so flexible that you can make it from both sets of inputs, with just one element in common?[1] And you do have to make it from those inputs if you are talking about converting the entire planet. You can't just say "it will refine the trace elements available" - this just results in trace amounts of nanobots on the surface of an otherwise largely unchanged planet.
But can't you just send different designs to different planets? That doesn't help either, even if we assume it is possible to build nanobots from all of those different sets of elements - and that's one hell of an assumption. Because then you just run into the same issue on a smaller scale - you'll have your Mars Pattern Nanobot, perfectly tuned to reflect the average composition of Mars (which includes 36% iron, 9% magnesium), sitting in the middle of a many kilometers-wide plain of nearly pure SiO4, and its sibling somewhere near the pole, surrounded mostly by H2O, neither quite sure what to do next.
Of course within one planet we can have nanobots shipping materials around. But to accomplish that, the they would likely need to combine into some sort of macro-scale agglomerates - for speed, energy efficiency and to easier overcome obstacles. They would probably also need to build or assemble some kind of clear passageways for the same reasons. And since so much of the input materials would need to be shipped in, it would only make sense to process it all in one place rather then re-distribute it evenly across a thin film of nanobots. But by that point if we have roads, trucks and factories, why exactly are we bothering with the "nano" part?
Alternatively, the problem can be solved if the nanobots can also do nuclear transmutation, converting elements into each other. But right now this is an absurdly inefficient process requiring giant particle accelerators, and to the best of my knowledge nobody has even a slightest idea of how (or if) it may be accomplished on the nano-scale and with a reasonable energy efficiency. Which brings us to the next problem.
Energy
In addition to raw inputs, nanobots need some energy to tear apart those constituent elements, assemble them into new nanobots or other useful stuff, and, since we're talking about converting the planets into a Dyson swarm or Matrioshka brain, also to launch the outputs into orbit. Each of these steps requires energy. Lets go over all possible energy sources.
Chemical - this is straight out because we are largely disassembling rock, and rock is at or near its thermodynamic floor. So is water which is the main component of crust of the outer moons. In fact, we will be spending a lot of energy just to tear those elements apart.
Nuclear fission - possible in principle, but it turns the element abundancy problem into an even bigger show stopper than before. Most places just don't have any meaningful amount of fissile fuel.
Nuclear fusion - one of the main difficulties with doing it on the macro scale is that the reactors we build are not big enough - and the reactors we build are the size of a building. Making it work on the nano-scale would be some magic-level technology indeed. And it also aggravates the material problem, though not to the same extent as fission, because deuterium is rare even on the bodies that do have water.
Solar - this is the only viable option with the technologies we can at least hypothesize as possible. Viable in the sense that we can be reasonably sure nanobots across all of the solar system can at least get some energy this way. Lets look at it a bit closer.
The very best place in the solar system to do solar-powered planet disassembly is the day side of Mercury. To further simplify the task, I'll only consider the energy cost of breaking down the rock into its constituent elements. I will ignore the cost of assembling them into a new configuration, as well as the cost of lifting the outputs into the Mercury's orbit. I'll also assume 100% efficiency for all the processes involved, from solar power collection to reducing the minerals.
The relevant numbers are: average solar flux at Mercury's orbit is 9000 W/m², chemical binding energy of rock is ~10 MJ/kg, and rock density is around 3000 kg/m³.⁶
To speed things up, we could build giant mirrors in orbit to focus solar energy on the planet, or better yet solar power arrays and emitters, converting it to some uniform wavelength which can be collected by our nanobots more efficiently. We'd need to have flight trajectories for whichever launch method we use clear of this massive flux of energy. And in any realistic scenario, we also need very large and very hot radiators to re-emit the waste heat. So the whole picture, again, begins to look less like a homogeneous and autonomous grey goo and more like a mega-scale logistics web with nanoassemblers being one node in it.
Conclusion
I'm not saying that nanoassemblers won't be an extremely useful tool in space colonization - obviously they will be. Being able to assemble anything from the raw materials using the same instrument, an instrument that can be scaled up or down smoothly and indefinitely, is a wildly beneficial capability to have in any situation, but in particular when colonizing extremely remote environments where nearly every task requires advanced technology.
And of course it is possible that a god-level ASI can invent nano-scale nuclear fusion and transmutation, or maybe even it can tell conservation laws to bugger off entirely. If you postulate this kind of power, forecasting is useless and worldbuilding is only limited by your imagination.
But within the limits of known or at least vaguely hypothesized physics, nanoassemblers will be just one tool in a toolbox, not a magic pill that you can drop on a planet, wait for a few years/decades, and come back to a planet mass worth of goodies. Even with this technology, seriously colonizing Solar System will require planetary and inter-planetary scale logistics in both matter and energy, and things like constructing a Dyson swarm would take at least multiple centuries, and more likely many, many millennia.
As mentioned, I'm making the task easier for nanobots by not considering the giant planets, even though they are 99% of the planetary mass. If we include them, it gets beyond hopeless since they are mostly hydrogen and helium - good luck making complex molecules out of those.
Speaking of surface: how do nanobots survive and how all those delicate large molecules continue to function at the Venus surface, with the temperatures higher than that of boiling oil? I've no idea. There is very little sunlight there anyway thanks to the thick atmosphere. Maybe you can get clever with nanobots floating in the upper atmosphere using oxygen as the lifting gas.