Traditional Kelly betting is about limiting your exposure to a risky bet. The bet in question is usually a "bet" in that when you lose, you lose everything you expose.
The optimal leverage here is less than 1. You want to hold cash on the side to buffer the future losses.
I showed here, that individual stocks are effectively full Kelly bets.
Just buying one stock is the appropriate "size", as they have an optimal leverage of 1.
In these cases the Kelly criterion says to increase exposure, not limit it.
Increasing exposure beyond what you own requires some else to lend you something. It requires other to be involved and other promises to be made.
Because of this, I feel that Kelly betting strategies that increase exposure are a slightly different animal than ones that limit exposure and need to be handled differently.