I think there will never be a fully automated and 100% effective anti-cheat solution, even console gamers can use aim assist devices like the Cronus Zen, and false positives seem to be a much worse problem in client side anti-cheats than on server side ones.
Under that premise, the best solution is a combination of getting a decent number of cheats detected automatically + getting a small number of cheats reported by players or flagged as suspicious due to improbable statistics and manually detected by support staff + getting a really small number of false positives that support staff can quickly manually review and revert.
Most companies don't even try, they spend 0$ researching server-side anti-cheat measures. The few cheaters I have seen on PC are not even slightly difficult to detect server side, like people teleporting, flying or moving at absurdly high speeds in Battlefield games.
I think machine learning could be of huge help in this matter, as a neural network properly trained could identify players behaviour when using a wallhack with a high degree of accuracy, for example. But it is easier to infect the player's computer with rootkits that don't even require per-game implementation and are mostly generic.
