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?
Or perhaps the 0ms-80ms distribution of mouse movement matches the >80ms mouse movement distribution within some bounds. I'm thinking KL divergence between the two.
The Kolmogorov-Smirnov Test for two-dimensional data?
There's a lot of interesting possible approaches that can be tuned for arbitrary sensitivity and specificity.
As always, one of the most difficult parts is getting good features and data. In this case one difficulty is measuring and defining the reaction time to begin with.
In Counter Strike you rely on footsteps to guess if someone is around the corner and start shooting when they come close. For far away targets, lots of people camp at specifc spots and often shoot without directly sighting someone if they anticipate someone crossing - the hit rate may be low but it's a low cost thing to do. Then you have people not hiding too well and showing a toe. Or someone pinpointing the position of an enemy based on information from another player. So the question is, what is the starting point for you to measure the reaction?
Now let's say you successfully measured the reaction time and applied a threshold of 80ms. Bot runners will adapt and sandbag their reaction time, or introduce motions to make it harder to measure mouse movements, and the value of your model now is less than the electricity needed to run it.
So with your proposal to solve the reaction time problem with KL divergence. Congratulations, you just solved a trivial statistics problem to create very little business value.
You arent eliminating cheaters, that's impossible, you are limiting their impact.