more likely volunteers when they're running their own servers

volunteers which aren't necessarly pro player and cant distinguish good players from smart cheaters.

The developers aren't pro players either, the cutting edge for anti-cheats still require that non-cheaters play with cheaters for months. I would not be shocked if simple vote-kick outperforms every anti-cheat on the market.

A simple vote-kick will kick, will kick so much players that doesn't cheat. It's already used to troll in games like CS.

Not really. In mostly player-run lobbies, one of the players would kick any found cheaters. It's not exacts science, but it's what people did.