Take note: Many BAT earners are moving their tokens into private wallets!
Something I recently noticed while checking out Etherscan: https://etherscan.io/token/0x0d8775f648430679a709e98d2b0cb6250d2887ef
Many BAT token holders are moving their earned BAT tokens into private wallets. This seems to be working exactly as intended. Alongside the amount of token holders steadily increasing, there are many Uphold -> private wallet transactions happening. On a large enough scale, this is exactly what token holders and the project would want to happen; distribution.
Numbers re; keeping the tokens in the system for payments are currently impossible to tell, but one can assume this is being done to a significant degree as well.