Kelly is special though, it's not just log utility. In fact, viewing it as maximizing log utility is ahistorical; the original derivation was in terms of information theory. (The paper's title is "A new interpretation of information rate" [0].) Further, and most importantly, Kelly betting has certain favorable asymptotic properties that betting strategies motivated by other utility functions don't have. See Breiman's "Optimal gambling systems for favorable games" [1].

This point is well known in the literature, for instance see [2]:

> Perhaps one reason is that maximizing E log S suggests that the investor has a logarithmic utility for money. However, the criticism of the choice of utility functions ignores the fact that maximizing E log S is a consequence of the goals represented by properties P1 and P2, and has nothing to do with utility theory.

[0] https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf

[1] http://www-stat.wharton.upenn.edu/~steele/Resources/FTSResou...

[2] https://pubsonline.informs.org/doi/abs/10.1287/moor.5.2.161