So the reason why Linux players can't play is because the anti-cheat hooks into the kernel of the OS. And the anti-cheat is made for the Windows kernel. It is entirely possible for them to make one that is compatible with Linux but they won't. Besides, hooking into the kernel does not offer complete protection against cheats.
So hooking into the kernel is unwarranted given that the anti-cheat software is potentially able to transmit malware and observe everything on your computer since it has direct access to the kernel, even though cheating is still possible.
EAC is one of the most popular anticheats and it has a Linux version. The hardest thing developers need to do is decide to allow Linux, the actual implementation takes less time than a coffee break.
What you're saying literally isn't true. For example you can play The Finals on Linux and that's a multiplayer only game.