Comment by ItsMonkk
The problem here appears to be the banning. If the cheaters are never banned then they will continue to only play with other cheaters, and everyone is happy. And in fact, to a normal player I doubt they care very much if the player is legit and smurfing or if they are not legit and cheating. That player ruins the game they are in.
The ranking system needs to be a better determinate of skill, especially early in a new accounts life, so that they can stop harming normal players games. This might mean changes to the rules of a game to allow this to be done better. The match-maker should take this into account, so that if a player does go up against a player that was far from the skill level that they end up at, it should protect that account from being placed with new players for a time so that they can forget about it.
For the example you choose for Chess, you might force players to do Chess Puzzles before they can queue for their first match. A normal player would then never see any cheaters.
Cheaters don't want to play against other cheaters. If they end up against only cheaters that's a kind of soft-ban or shadow-ban and once they figure out that's the case they'll do the same steps as if you had actually banned them. It also angers legitimate players to know that the top ladder tier is for cheaters only. If you're 200th in the world and legitimate, other players will say you only got that rank through cheating.
And the very best cheaters are still good at the games they cheat in, they just want to use cheats to be even better. One famous example in a game I play is Riolu in Trackmania. He was probably one of the top 10 players in the world. But he wanted to be #1. When he was accused of cheating it took a mountain of evidence for anyone to believe the accusations because he could set a world record live in-person. He just used cheats to be able to do it with fewer attempts.