Anti cheat is about the only thing that doesn't work but I see that as a bonus. Anti cheat is more like a virus than it ever has been with the rootkit thing.
EAC and Battleye both can work with Proton, the developers just need to set it up. Those two cover most of the gaming anticheat market. Battleye should be as simple as the dev telling Battleye to turn on Proton support and EAC should be an SDK upgrade.
It's all relatively easy to support Linux, people just need to pressure developers to make it happen.