Online multiplayer games must (yes must) take place on servers with human admins. Admins should be present for a majority of the time any players are playing.
Ideally with admins the players recognize. Bonus points if players themselves can perform some moderation when no admin is present (votekick, voteban etc). There is no difference between kicking cheaters and kicking people who are abusing chat etc. Obviously this means that "private" or "community" servers are the only viable types of server for online multiplayer games.
This process of policing cheaters and other abuse can not be something that is done via a reporting system and handled asynchronously. Kicking/banning must be done by the admins of the game, and it must be handled quickly.
If you are considering buying/playing an online multiplayer game and it doesn't have this functionality (e.g. the only way to play online is via matchmaking on servers set up by the publisher, and the only way cheaters and chat abusers are policed is via some web form) then please, avoid that game. Vote with your wallet.