I have never seen cheaters being an issue (even the few times people set up tournaments with prizes), which makes me think that this might be limited to very few games (in very specific genres) ?
Yes. Every game has cheats. The cheat packages are pretty easy to adapt to new games and people pay money for them.
Why do people cheat? Because it’s fun! If you’ve never cheated it’s honestly worth trying. It’s hilarious. It also utterly ruins the game for everyone else in the lobby.
If games had reliable anti-cheat you’d be shocked at the percentage of lobbies that have a cheater. It’s wildly rampant.
But a lot of games do also have accessible to everyone replays that show every order given by every player, so catching a cheater that acted on information not available to them (because for instance they had buddies in other team(s)) isn't particularly hard, especially in tournaments with a lot of eyeballs on those replays.
At scale it’s incredibly hard. Impossibly hard even. So hard no one has successfully solved it! Ever!
But what you’re describing is Valve’s Overwatch system for Counter-Strike. It’s a key component of the anti-cheat ecosystem. But cheating is still rampant in CS and one of the biggest complaints.
I take this opportunity to share this great talk about Valve's usage of deep learning to fight cheating in CS:GO: https://www.youtube.com/watch?v=kTiP0zKF9bc
And "at scale" pretty much means that matches are not competitive, because the sums required for entering a tournament game and given for winning it are going to be too small, won't they ?
P.S.: And for non-competitive games, I would expect that this cheating issue (among others) would be aggravated if you insist on playing with total strangers you will never see again (also part of the scale issue) - maybe just avoid that ?
Part of the appeal for cheating is doing it where it has impact - in popular games.
Also, I want to insist on one thing : some of the popular games listed are those that are online-only and/or removed the ability to host your own servers (and/or even worse, have microtransactions).
I have zero sympathy for the kind of asshole that gave money to companies engaging in the despicable behaviour cited above. You were warned. You made your own bed, now lie in it !