I don't see how public servers and matchmaking are an issue. The public servers that are known to tolerate cheaters are themselves just going to get a bad reput

I don't see how public servers and matchmaking are an issue. The public servers that are known to tolerate cheaters are themselves just going to get a bad reputation. The issue is the kind of game that doesn't allow you to host public servers, and which instead has an automatching system with an undisclosed algorithm. And since this also tends to be the kind of game that has DRM, doesn't even allow offline/private servers (is online only), and worse, engages into microtransactions and gambling, the sooner these games are made illegal, the better off the society will be.