On the other hand, you have issues like smurfers who cause the same disruption without actually running any cheat software.
Ultimately your problem is uneven matchmaking and the perception of cheating, not cheating itself.
Especially with gaming becoming mainstream compared to early 2000s. The majority of players are now casual gamers who are not interested in a job as a server admin/hoster.
Unironically, Cloud gaming. Stadia had a terrible business model, but the tech worked. Microsoft's XCloud together with GamePass could be a winning ticket for that. (I think there's also GeForce Now)
Of course, that wouldn't prevent anyone from capturing the screen, running image recognition software on the screen and sending USB Controller inputs to create an Aim Bot, but then again, that's not something anti-cheat software can stop these days anyway.
Ironically, cloud gaming is the perfect solution for single-player game, where input lag and high FPS doesn't matter much.
The freedom afforded in personal computing by Windows and Linux is fundamentally mutually exclusive to the security that multiplayer game operators and proper players legitimately need.
It's why game consoles and mobile gaming are the core gaming platforms. Note how Sony and Microsoft blacklist consoles suspected to be used by cheaters, and how games (and also banking) absolutely hate rooted smartphones because it breaks the assumption of a locked down and secured system.