One very critical factor you forgot is goal uncertainty! Your argument is actually even better than you think it is. If you assign an extremely low but non-zero probability that your utility function is unbounded, then you must still multiply it with infinity. And 1 is not a probability... There is no possible state that represent sufficient certainty that your utility function is bounded to justify not giving all your money to the mugging.

I WOULD send you my money, except the SIAI is a lot of orders of magnitude more likely than you to be a god (you didn't define it'd be instant or direct) and they have a similar offer, so I'm mugged into maximizing amount of help given to the SIAI instead. But I DO bite the bullet of small probabilities of extremely large utilities, however repugnant and counter-intuitive it seems.