Recent testing revealed that Arch Linux, Pop!_OS, and even Nobara Linux, which is maintained by a single developer, all outstripped Windows for the performance crown on Windows-native games. The testing was run at the high-end of quality settings, and Valve's Proton was used to run Windows games on Linux.
In the defence of client side AC; if the entire game runs on the server, then network delay makes FPS:es awful to play. Being able to trust clients and let them do hit detection is quite important in making online FPS:es responsive. In addition, cheats that remove walls/grass, highlight players or even autoaim are near impossible to detect server side. One could try to use heuristics and statistics but it would be difficult to tell the difference between cheaters and players who are just good at aiming and map awareness.