I think that would make Linux players into second-class citizens who could only play in a pool that is 90+% filled with Windows cheaters.

Segregating into two pools: Windows-verified, or Linux-unverified, would probably not work for Linux users either. It'd be the same problem (on a smaller scale) as not including kernel anticheat in Windows. No fun for the non-cheaters.

I'm not a gamer though, so I may be missing important details.