Still...
My "new set of indices" comment was in the context of "risk athirst" strategies -- ie. clearly outside the CRRA domain. I have seen texts on utility theory that specifically discuss risk prone strategies, and label them "rational."
Actually, a "risk athirst" strategies are also part of power utility functions, where U(x) = x^p/p for p>0. For p=0 we get log, which I assert is still not reasonable. A reasonable personal power starts around -3 (fourth Kelly), but in the long run more like -9 or -14 (tenth Kelly, 1/15 Kelly).
Nevertheless, you get the same indices even for p>0. The point is that you just grossly overbet.
I agree that theoretically, the indices could differ for other utilities than CRRA (which include "risk athirst" CRRA). But the point is that it is a second order difference, and I conjecture that it would be completely negligible.
Karel