Well yeah, you can't expect a third-party anti-cheat to solve all of your problems, each game is going to have idiosyncrasies.

I think Valve's Overwatch system is a fantastic example of ways to innovate without compromising a user's security or requiring platform-specific cheat detection. It's probably not enough on its own (those reviewers need data), but to me it's preferable to something more invasive like BattleEye. A lot of that can be done server-side, by running player movements through an AI model that detects players that fit certain patterns, or don't fit common patterns.