I think the problem of designing and building self replicating probes, capable of recreating themselves from asteroidal matter, is greatly underestimated. We currently have little to no idea how to design such a thing, and no real idea what the lower bound on the mass of such a thing might be.
The next problem is nterstellar travel. The difference un scale between traveling to the moon and travelling to a nearby star is about the same difference in scale between throwing a rock down a typical garden and launching astronauts to the moon. The Daudalus project did down good work on this and their very modest proble of just a few tons, doing a flyby of a nearby star, took a large to portion of the mass of Neptune to construct in terms of fuel. The resources available in a typical planetary system might not be up to the job.
I don't honk magic future technology hand waves these problems away. Any future technology will have to work with the same elements on the same periodic table we have now, manipulating the same physical forces we work with now. We can't wish magic unobtainable into existence and the limits of what is achievable with matter and energy are already pretty much computable.
So it really may well be that going sustainably interstellar might be impractical.