This isn't really true. As GP said, there isn't a kernel level anti cheat for linux. You can switch a flick on BattleEye to run on linux but it wont be a kernel level as it is on windows. So there is an incentive for them to not turn it on because it simply is the worse version than the windows one. As far as I know even on windows you get cheats even if it is kernel level. Meaning, allowing linux you'd probably be flooded with cheaters if you already get them on windows.
There's an easy way to not get cheaters, or at least to slow down their impact: stop making your games "free to play". When cheaters have to buy 60€ games everytime they get b&, eventually they'll run out of money.