It would be ruinously costly to send over a large colonization fleet, and is much more efficient to send over a small payload which builds what is required in situ, i.e. von Neumann probes.
I would disagree on large colonization fleets being ruinously expensive, the best case scenario for large colonization fleets is if we have direct mass to energy conversion, launching say 2 probes from each star system that you spread from. Each probe would use half the mass energy of the star. Converting a quater of its mass to energy to get ~0.5c
You can colonize the universe even if you insist on never going to a new star system without bringing a star with you. (Some optimistic but not clearly false assumptions)
Accelerating a probe to ~0.5c isn't the biggest issue. It will be much harder to deaccelerate once you are at the target location.
For some destinations, but not for most of them (I'm pretty sure). At least Eternity in Six Hours spends a great detail of time discussing deceleration.
The main assumption, imho, is that if we input very large capabilities, we will get very large achievements. That is, if we we assume possibility of superintelligence and nanotech, we will get a possibility of quick intergalactic travel.
However, arguing from infinities could be problematic, as it could produce contradicting results, as is well known in the philosophy: https://en.wikipedia.org/wiki/Omnipotence_paradox
This is a list of claims and assumptions made in the FHI paper, Eternity in Six Hours. It is not exhaustive. I collected this list as part of my attempt to answer the questions:
Since my interest is writing this is on the feasibility of intergalactic colonization, I've neglected claims in the paper about the Fermi paradox.
The Fermi paradox is the discrepancy between the strong likelihood of alien intelligent life emerging (under a wide variety of assumptions), and the absence of any visible evidence for such emergence. In this paper, we extend the Fermi paradox to not only life in this galaxy, but to other galaxies as well. We do this by demonstrating that traveling between galaxies – indeed even launching a colonisation project for the entire reachable universe – is a relatively simple task for a star-spanning civilization, requiring modest amounts of energy and resources. We start by demonstrating that humanity itself could likely accomplish such a colonisation project in the foreseeable future, should we want to, and then demonstrate that there are millions of galaxies that could have reached us by now, using similar methods. This results in a considerable sharpening of the Fermi paradox. [emphasis added]