An interesting argument, and a good intuition for why the Kelly criterion is good.

As far as it relates to my comment and comment: I think you're advancing a third answer to the "why" question, not showing why "maximizing expected geometric growth" is a better "why" than "maximizing (logarithmic) utility".

With that said, I still think the "maximizing (logarithmic) utility" answer is the only good motivation. My reasoning is that most people (myself included) define rationality to be: maximizing expected utility. From this, we can derive the Kelly criterion.