Although this is true for most games it is worth noting that it isn't universally true. Usermode anti-cheat does sometimes work verbatim in Wine, and some anti-cheat software has Proton support, though not all developers elect to enable it.
Because of that, usermode anti-cheat is definitely far from useless in Wine; it can still function insofar as it tries to monitor the process space of the game itself. It can't really do a ton to ensure the integrity of Wine directly, but usermode anti-cheat running on Windows can't do much to ensure the integrity of Windows directly either, without going the route of requiring attestation. In fact, for the latest anti-cheat software I've ever attempted to mess with, which to be fair was circa 2016, it is still possible to work around anti-cheat mechanisms by detouring the Windows API calls themselves, to the extent that you can. (If you be somewhat clever it can be pretty useful, and has the bonus of being much harder to detect obviously.)
The limitation is obviously that inside Wine you can't see most Linux resources directly using the same APIs, so you can't go and try to find cheat software directly. But let's be honest, that approach isn't really terribly relevant anymore since it is a horribly fragile and limited way to detect cheats.
For more invasive anti-cheat software, well. We'll see. But just because Windows is closed source hasn't stopped people from patching Windows itself or writing their own kernel drivers. If that really was a significant barrier, Secure Boot and TPM-based attestation wouldn't be on the radar for anti-cheat vendors. Valve however doesn't seem keen to support this approach at all on its hardware, and if that forces anti-cheat vendors to go another way it is probably all the better. I think the secure boot approach has a limited shelf life anyways.
Any player responding to ingame events (enemy appeared) with sub 80ms reaction times consistently should be an automatic ban.
Is it ever? No.
Given good enough data a good team of data scientists would be able to make a great set of rules using statistical analysis that effectively ban anyone playing at a level beyond human.
In the chess of fps that is cs, even a pro will make the wrong read based on their teams limited info of the game state. A random wallhacker making perfect reads with limited info over several matches IS flaggable...if you can capture and process the data and compare it to (mostly) legitimate player data.
Can you define what "reacting" means exactly in a shooter, that you can spot it in game data reliable to apply automatic bans?
A human can't really, which is why you need to bring in ML. Feed it enough game states of legit players vs known cheaters, and it will be able to find patterns.