The motivation of your post - the fact that fallback is not necessary with many proportional pools - is not new. I've said this already here (Table B.1) and before that.

The reason it's unnecessary because when there are many pools, you never get to 43.5% - there will virtually always be a pool with less than that. So you don't need any of the "random threshold selection from the range [0.5, 1.5]" nonsense.