This depends on the distinction between a player having infinite plays (in which case the optimal strategy is to bet their minimum infinity times), and the player having a finite number of plays but considering the optimal play as that finite number of plays approaches infinity. It's not intuitive, and in retrospect, I think I could have explained it better in the post.

The assumption is that you want the maximum return for any given number of bets. If you have unlimited bets then sure, maximizing the return per bet is not really important. But where can you find unlimited bets with positive expected return?

There are other assumptions in there, like that there's no minimum bet and you can divide your bet to arbitrary precision. Always check your assumptions! I'm sure someone has modified the Kelly criterion for minimum bets and quantized bets, but a cursory search didn't turn it up immediately.

That assumption was never stated in the question. It didn’t say there was any cost to placing a bet, and I learned quite quickly that I could mash the bet button very fast… why would I take any risk at all when I can get a guaranteed win betting small and mashing the button?

Yep just bet a dollar every time. Over enough presses you’ll see the law of large numbers guarantee you getting something that looks like exponential growth.

If you bet a dollar every time, you'll average $0.60 of growth every click no matter how much money you accumulate. That is linear growth, not exponential.

That’s right. If you bet 10% every time you’d get exponential growth.