Epistemic status: has "time travel" in the title.
Let's suppose, for the duration of this post, that the local physics of our universe allows for time travel. The obvious question is: how are paradoxes prevented?
We may not have any idea how paradoxes are prevented, but presumably there must be some prevention mechanism. So, in a purely Bayesian sense, we can condition on paradoxes somehow not happening, and then ask what becomes more or less likely. In general, anything which would make a time machine more likely to be built should become less likely, and anything which would prevent a time machine being built should become more likely.
In other words: if we're trying to do something which would make time machines more likely to be built, this argument says that we should expect things to mysteriously go wrong.
For instance, let's say we're trying to build some kind of powerful optimization process which might find time machines instrumentally useful for some reason. To the extent that such a process is likely to build time machines and induce paradoxes, we would expect things to mysteriously go wrong when trying to build the optimizer in the first place.
On the flip side: we could commit to designing our powerful optimization process so that it not only avoids building time machines, but also actively prevents time machines from being built. Then the mysterious force should work in our favor: we would expect things to mysteriously go well. We don't need time-travel-prevention to be the optimization process' sole objective here, it just needs to make time machines sufficiently less likely to get an overall drop in the probability of paradox.
We would also expect destroying time machines to be a convergent instrumental goal in this universe, since any agent that does this would be more likely to have been created. So by default powerful enough optimization processes would try to prevent time travel.
Let us suppose <impossible thing>. Now <impossible result> remains impossible, how? Maybe the universe has a mysterious agency we can trick or bargain with!
I think you'll need to back up a bit further if you want to explore this. "time travel is possible" isn't well enough defined to be able to reason about, except in the human conceptual space with no physics attached. And if you're assuming away physics, you don't need to explain anything, just let the paradoxes happen.
Are you familiar with the Gödel metric? Time travel may well be impossible, but at least within the context of general relativity it is plenty well-defined to reason about.
Does Gödel metric say anything about prohibition of paradoxes?
I have found that assigment of 0 to a paradoxical configuration is an opinion or assumption and not a result or a theorem.
For example the electron wave function negative solutions were dismissed as unrealistic math artefacts at one point and later adopted as a valid way to reason about positrons. Would it have been correct to say that "obviously electrons have a negative charge?. In modern terms you can distinguish between claims of "leptons have negative charge" and "electrons have negative charge". But if the only lepton you know is an electron is "positive electron" a valid thing?
While things add up to normality unusual circusmstances can exhibit unsual phenomena.
The real question here is what mechanics + GR "says" about paradoxes; there's nothing special about the Gödel metric other than that it's a specific example of a system containing closed time-like loops.
The answer is that mechanics + GR cannot represent a system containing a paradox, at all. We just have a bunch of particles and/or fields moving around a space with a metric. The local laws of mechanics + GR constrain their behavior. A "paradox" would, for instance, assert that there is a particle at (x, t) with velocity v, but also not a particle at (x, t) with velocity v - the underlying theory can't even represent that.
We don't know how to integrate QFT with GR, but conceptually a similar problem should arise: we just have some quantum fields with complex amplitudes at each point in spacetime. A paradox would assign two different amplitudes to the field at the same point. Again, our physical models can't even represent that: the whole point of a field is that it assigns an amplitude at each point in spacetime.
We could maybe imagine some sort of multivalued state of the universe, but at that point our "time machine" isn't actually doing time travel at all - it's just moving around in a somewhat-larger multiverse.
As we lack the means to represent the different options we probably do not have a law that paradoxes will be avoided (partly because we do not have a technical analogoue for "paradox")
In the extended ontology what corresponds to old time would be an open question. That is if you have a multivalued state in the past and some of the values of that are effects of (partial) values in the future it's still pretty much "time travel".
I also thought that qunatum mechanics is pretty chill with superposition. Could not one extend the model by having a different imaginary unit and then have a superposition of amplitudes? And I thought getting a sure eigenvalue is a special case. Isn't the non-eigenvalue case already covering a simultanoues attribution of multiple real values? I case there are two cases 1) we do not represent that currently in our models or 2) Our representations used in our models can not represent that.
Having played Achron I have visited the thought space a lot before.
The thing that allows for time travel might break a lot of your other presumptions. If the moon was made of cheese were would all the milk would have come from?
I would like to point out that the assumtion that timelines are stable is a separate assumption from time travel. I think it needs argument and argument from lack of imagination is not a very convincing one.
However even if you go outside of this assumtion were similar things still happen. In another attempt one could argue that if a grandafther paradox has 2 viable states then both of those states should sum in probablity to a state that is "stable". So you assign less probability to things that can grandfather paradox. If a thing can attempt to paradox in multiple ways you have keep splitting the "measure". The end result is that a thing that can constantly paradox will be vanishingly unlikely to hang around. This is different than "mysteriously prevented" but for these purposes serves a similar function.
After all if quantum superpositions are not prevented why would "timeline superpositions" be incompatible?
It is noteworthy that invention of timetravel technology is an event that probably has causes. Anything that utilises such technology would be causally dependent on that event. But that even is causally dependent on other events. Thus it might be counterproductive to have any timetravel technology effect any cause of time travel technology. This would effectively mean that all of pre-timetravel history would be "natural reserve" on the pain of death of all timetravel history.
The is a reverse effect where is a time machine can help with its construction it might be tempted to do so provided it doesn't undo it more than do it. Even the slightest chance of a working time travel method would be blown to optimally early time travel (within the constraints).
That is fiction has plenty of timetravel reasoning to throw around. Specifying your poison would go for a long way. For example rpg game continuum has slipshanking. Having a sudden fight? Grab a pistol from nearest container. Then after fight go to a shop buy gun, go to past and put gun into said container. Timeline is stable, but it feels weird taht realising that you could try do somethign makes it possibel for you to do so (this kind of reasoning has limitations, if you have openend the box and seen it empty you obviosly can't slipshank a pistol out of it. But being strategically ignorant in order to maximise slipshanking possiblities is interesting). The ultimate slipshank would be to do it before time travel is invented with the intention to invent time travel to pull it off