For example, suppose you have a bet that has a 50% chance of losing everything and a 50% chance of quadrupling your investment, the Kelly criterion says not to take it, since losing everything has infinite disutility.

A bet where you quadruple your investment has a b of 3, and p is .5. The Kelly criterion says you should bet (b*p-q)/b, which is (3*.5-.5)/3, which is one third of your bankroll every time. The expected value after n times is (4/3)^n.

The assumption of the Kelly criterion is that you get to decide the scale of your investment, and that the investment scales with your bankroll.

If you take it n times, you have a 2^(-n) chance of having 4^n times as much as you started with, which gives an expected value of 2^n.

Indeed, but the probability that the Kelly better does better than that better is 1-2^(-n)!