First of all, I really don't understand why some games require anti-cheat to even start. If someone is playing single player, or using a private server or lan, who cares! Let them cheat if they want to, or run on linux where anti-cheat isn't possible.

Secondly, unless there are monery awards for winning or something, is it really that big of a problem if people cheat? If you are playing against a stranger, is there a significant difference between playing against someone of the same skill level with cheats, and someone that is much better than you? With a good bracketing system, people who cheat will either end up against other people who cheat, or people who are good enough to play against cheaters. You could also do things like let player opt in to using anti-cheat software, and then only play against other players with anti-cheat software. Or even have arenas specifically for people who use cheating software, for people who think that makes the game more fun.

There are RPGs in which you don’t play against other people but you can interact with them to sell items. In these games being able to generate vast amounts of in game wealth creates inflation for everybody and makes it so that normal players can’t interact with the economy. With regards to your other point about separating the player base it would create fragmentation and higher queues for matchmaking. Finally keep in mind that even in single player games people compete for speed run records or world first achievements.