> It's not the fault of Linux for refusing to allow this.
Linux doesn't refuse anything, it's free and open source software. If publishers want to offer anti-cheat software developed for Linux, it will run. In fact, many games do have anti-cheat, like Insurgency: Sandstorm, which uses EAC through Proton.
Publishers can even develop invasive kernel-level anti-cheat just like they do for Windows. They don't because it's a small portion of the market currently, and I assume they consider it not worth the investment as of now. To what extent existing Linux users would willingly allow such software to run is also an open question.
There's also the point that even invasive kernel level anti-cheat on Windows with requirements for secure boot continues to be inadequate to stop cheaters in competitive online games.