One particular objection: the fact that evolution has gotten us here contains a fair bit of anthropic bias. We don't know exactly how narrow are the bottlenecks we've survived already.

Well, I don't want to appear to endorse the thesis that you associated me with - but it appears that while we don't know much about the past exactly, we do have some idea about past risks to our own existence. We can look at the distribution of smaller risks among our ancestors, and gather data from a range of other species. What Joshua Zelinsky said about genetic data is also a guide to recent bottleneck narrowness.

Occam's razor also weighs against some anthropic scenarios that imply a high risk to our existence. The idea that we have luckily escaped 1000 asteroid strikes by chance has to compete with the explanation that these asteroids were never out there in the first place. The higher the supposed risk, the bigger the number of "lucky misses" that are needed - and the lower the chances are of that being the correct explanation.

Not that the past is necessarily a good guide - but rather we can account for anthropic effects quite well.