A lot of the mathematics are uncomputable in some situations. There are a lot of cases where you simply don't know enough to actually do Bayes' theorem, but knowing about it, and understanding the process behind it, makes your own thinking that much better. Solomonoff induction may be incomputable, but if you get the purpose behind it, or you use an approximation, that's good enough. Much of the theoretical ideas are difficult to use in real life situations. Approximate. Do the absolute best that you can to solve the problem.

Finally,

And what about what I really want to do, intuitively, should I just ignore that?

If what you intuitively want to do is going to lead you to not fulfill your goals, yes. If you've determined that acting on instinct is better in a given situation, by all means do it. Win.