> increasing populations make things look more Gaussian - in all natural circumstances.

This is just not the case, there's plenty of "natural circumstances" where populations have non-Gaussian distributions.

Perhaps you meant a specific type of population, like chess ratings? I'd be interested in seeing what you find there, but all I've found shows significantly distorted tails (not to mention a skew from 1500).

Both for sure. If you don't practice you will never rise much about bad. But if you are bad and not progressing you won't play much because it isn't rewarding to lose.

One needs to almost figure out those with low ELO ratings, what is their history compared to the number of games played and see if they were following an expected ELO progression.

I wonder if you can estimate with any accuracy where a player will eventually plateau given just a small-ish sampling of their first games. Basically estimate the trajectory based on how they start and progress. This would be interesting. Given how studied Chess is, I expect this is already done to some extent somewhere.