This also lets in stupid problems, like "you get a dollar iff the source code to your decision theory is prime", which I would classify as not a decision theory problem at all.

In this case, the outcome is the same for every action you make. A decision theory can still consider this problem, and rightfully conclude that it's irrelevant which action it takes (or maybe it infers that jumping on a right foot has a slightly higher chance of making Dark Lords of the Matrix to have written your source code so that it's prime). I don't see how this is a problem.