> why should it not be the default?Why should what not be the default? The speculations of string theory? Um, because they're speculations?
>* just the idea there is something that doesn't collapse any further*
Because our best current theories, the ones we have actually tested experimentally, say that once you are over the maximum mass limit of stable states of matter, there is no alternative to collapse to a black hole.
If someone comes up with a better theory that makes different predictions, and has that better theory confirmed by evidence, then our default will change. But until that happens, our default is what our best current theories that have been confirmed by evidence say.
> what are the testable consequences of the contrary - i.e. the existence of a singularity or the possibility of crossing the event horizon?
We cannot directly observe events at or below the event horizon from the outside, but we can test for the possibility indirectly by looking for the evidence that we would expect to see if something else happened, i.e., evidence that collapse stops somewhere short of the horizon. So far, in cases of objects which are above the known maximum mass limits, we have seen no evidence that anything stops the collapse short of the horizon. If we ever do see such evidence, it will be evidence that our best current theories need to be modified. But so far, as I have said, we have not seen any such evidence.
Speculating about other possible theories, in the absence of any evidence such as I have described, is fine as long as they are understood to be speculations. But in the absence of such evidence, the "default" remains as I have stated it above.
> Reading popularized accounts of renormalization gave me the idea that when a physical theory spits out infinities, it's got to be inadequate.
Not inadequate; incomplete. Yes, physicists pretty much agree that GR must be incomplete because it predicts infinities in certain particular regimes. But that only means the theory is incomplete in those regimes: at the singularities predicted at the centers of black holes. The black hole event horizon is not such a regime; GR predicts no infinities there whatsoever. So there is no reason to consider GR incomplete at the black hole event horizon, or even well below it, all the way down to the singularity, on these grounds.
> Whatever ideas don't give infinities are probably better.
Not at all. The fact that a current theory is believed to be incomplete because it has infinities in a particular regime, does not at all imply that any theory that does not have infinities in that particular regime must be better. That is simply faulty logic. The fact that many string theorists proclaim it does not make the logic any less faulty.
> relativity is guaranteed to be wrong
No, relativity is believed to be incomplete in one particular regime. That is very, very different from "wrong".