Client-side anti-cheat is a futile endeavor these days and besides being ineffective probably is user-hostile too. Server-side machine learning is the way to go.
Also the server should not send info a legitimate client have no use of.
> If it has 99% accuracy, then you're banning thousands of players
Obviously you can't just automatically permaban people if the system is not based on a technical inspection of the player's system. Instead you have to bar them from playing for a few days or so.
Even VAC reverses bans sometimes.
If you are looking for a perfect solution there will never be one.
> do not games send "too much" in order to play around networking constrains?
Maybe the newest games does that. CSGO and other popular games send complete positions and what-not to every player.
Also the server should not send info a legitimate client have no use of.