Yes, we do: bounded utility functions work just fine without any mathematical difficulties

And so does speed prior.

Realistic amounts of evidence won't be enough to neutralize 1), but would easily neutralize 2).

Yes. I have an example of why the intuition "but anyone can do that" is absolutely spot on. You give money to this mugger (and similar muggers), then another mugger shows up, and noticing doubt in your eyes, displays a big glowing text in front of you which says, "yes, i really have powers outside the matrix". Except you haven't got the money. Because you were being completely insane, by the medical definition of the term - your actions were not linked to reality in any way, and you failed to consider the utility of potential actions that are linked to reality (e.g. keep the money, give to a guy that displays the glowing text).

The intuition is that sane actions should be supported by evidence, whereas actions based purely on how you happened to assign priors, are insane. (And it is utterly ridiculous to say that low probability is a necessary part of Pascal's wager, because as a matter of fact, probability must be high enough.) . I have a suspicion that this intuition reflects the fact that generally, actions conditional on evidence, have higher utility than any actions not conditional on evidence.