Most of the arguments for Kelly betting that you address here seem like strawmen, except for (4), which can be rescued from your objection, and an interpretation of johnswentworth’s version of (2), which you actually mention in footnote 3, but seem unfairly dismissive of.
The assumptions according to which your derived utility function is logarithmic is that expected utility doesn’t get dominated by negligible-probability tail events. For instance, if you have a linear utility function and you act like it, you almost surely get 0 payout, but your expected payout is enormous because of the negligible-probability tail event in which you win every bet. Even if you do Kelly betting instead, the expected payout is going to be well outside the range of typical payouts, because of the negligible-probability tail event in which you win a statistically improbably number of bets. This won’t happen if, for instance, you have a bounded utility function, for which typical payouts from Kelly betting will not get you infinitesimally close to the bounds. The class of myopic utility functions is infinite, yes, but in the grand scheme of things, compared to the space of possible utility functions, is very tiny, and I don’t think it should be surprising that there are relatively mild assumptions that imply results that aren’t true of most of the myopic utility functions.
In footnote 3, you note that optimizing for all quantiles simultaneously is not possible. Kelly betting comes extremely close to doing this. Your implied objection is, I assume, that the quantifier order is backwards from what would make this really airtight: When comparing Kelly betting to a different strategy, for every quantile, Kelly betting is superior after sufficiently many iterations, but there is no single sufficient number of iterations after which Kelly betting is superior for every quantile; if you have enough iterations such that Kelly betting is better for quantiles 1% through 99%, the alternative strategy could still be so much better at the 99.9% quantile that it outweighs all this. This is where the assumption that negligible-probability tail events don’t dominate expected value calculations makes this difference not matter so much. I think that this is a pretty natural assumption, and thus that this really is almost as good.
Most of the arguments for Kelly betting that you address here seem like strawmen, except for (4), which can be rescued from your objection, and an interpretation of johnswentworth’s version of (2), which you actually mention in footnote 3, but seem unfairly dismissive of.
The assumptions according to which your derived utility function is logarithmic is that expected utility doesn’t get dominated by negligible-probability tail events. For instance, if you have a linear utility function and you act like it, you almost surely get 0 payout, but your expected payout is enormous because of the negligible-probability tail event in which you win every bet. Even if you do Kelly betting instead, the expected payout is going to be well outside the range of typical payouts, because of the negligible-probability tail event in which you win a statistically improbably number of bets. This won’t happen if, for instance, you have a bounded utility function, for which typical payouts from Kelly betting will not get you infinitesimally close to the bounds. The class of myopic utility functions is infinite, yes, but in the grand scheme of things, compared to the space of possible utility functions, is very tiny, and I don’t think it should be surprising that there are relatively mild assumptions that imply results that aren’t true of most of the myopic utility functions.
In footnote 3, you note that optimizing for all quantiles simultaneously is not possible. Kelly betting comes extremely close to doing this. Your implied objection is, I assume, that the quantifier order is backwards from what would make this really airtight: When comparing Kelly betting to a different strategy, for every quantile, Kelly betting is superior after sufficiently many iterations, but there is no single sufficient number of iterations after which Kelly betting is superior for every quantile; if you have enough iterations such that Kelly betting is better for quantiles 1% through 99%, the alternative strategy could still be so much better at the 99.9% quantile that it outweighs all this. This is where the assumption that negligible-probability tail events don’t dominate expected value calculations makes this difference not matter so much. I think that this is a pretty natural assumption, and thus that this really is almost as good.