I agree with the points about Boltzmann Brains and mind substrates. In those cases, though, I'm not sure the FAI heuristic saves you any work, compared to just directly asking what the right answer is.

The ideal FAI wouldn't care about its personal identity over time

Almost certainly not true if taken verbatim; one of the critical traits of an FAI (as opposed to a regular AGI) is that certain traits must remain stable under self-improvement. An FAI would care very strongly about certain kinds of changes. But with a less literal reading, I can see what you're going for here - yes, an ideal FAI might be indifferent to copying/deletion except to the extent that those help or hinder its goals.

I'm not sure how that belief, applied to oneself, cashes out to anything at all, at least not with current technology. I also don't see any reason to go from "the FAI doesn't care about identity" to "I shouldn't think identity exists."

The ideal FAI would use UDT/TDT/etc. Therefore I should too.

(Disclaimer: I am not a decision theorist. This part is especially likely to be nonsense.)

You should use which one?

The less snappy version is that TDT and UDT both have problem cases. We don't really know yet what an ideal decision theory looks like.

Second, I doubt any human can actually implement a formal decision theory all the time, and doing it only part-time could get you "valley of bad rationality"-type problems.

Third, I suspect you could easily run into problems like what you might get by saying "an ideal reasoner would use Solomonoff Induction, so I should too". That's a wonderful idea, except that even approximating it is computationally insane, and in practice you won't get to use any of the advantages that make Solomonoff Induction theoretically optimal.

If you instead mean things like "an ideal FAI would cooperate in PD-like scenarios given certain conditions", then sure. But again, I'm not sure the FAI heuristic is saving you any work.

The ideal FAI would ignore uncomputable possibilities. Therefore I should too.

A factual FAI might, for mere practical reasons. I don't see why an ideal FAI normatively should ignore them, though.