The Kelly Criterion derives from a model that differs from JD's real situation in a couple of important ways.

First, in the Kelly model, the player with the edge controls the betting.  Since he has an edge, he keeps on betting.  In contrast, with JD the house has the edge but must wait passively for the whales to bet.  Since the whales don't have an edge, they can and should stop when they're ahead.

Second, the Kelly model runs on "bet time", where the unit of time is one bet.  The Kelly Criterion maximizes the return over the number of bets.  In contrast, JD runs on "calendar time".  Investors count their return in percent per day or month or year, and count their opportunity cost the same way.

Because of these differences, it does not follow that setting the maximum bet based on the Kelly Criterion will maximize JD's return in calendar time. 

The maximum bet policy has been questioned before, and it's always been answered by an appeal to the Kelly Criterion, or to simulations based on the Kelly model.  I'm suggesting that the model doesn't match the reality, so it's time for a fresh look.