That is not easy. Linux is about having full control over our own hardware. Client-side anti-cheats are about preventing user of having full control of the system.
Especially the kernel-side anti cheats rely on kernel not being controlled by the user.

A few of them did. The problem is also implementation in the games.

In the past few months, I've been able to play more multiplayer games in Linux than before (notably Insurgency and Squad now work).

I tend to mostly play single player, but all in all, I don't even remember when I last booted my Windows partition. If it wasn't for a last glimmer of hope of reviving my Oculus CV1, I'd probably wipe it.

I think they are doing all they can. The major anti cheat systems already support Linux. It's just a matter of the game devs actually allowing Linux.

Even Microsoft did that for Halo.

That's the last of the big walls, but unfortunately there is still work to be done.
The main problem I see is that most of the support is through proton, and often almost all the work is done by valve. Without native games (well ported) the performance is inferior.

Oh, and nvidia, damn nvidia.