User reports are indeed a common tranche of anti-cheat systems.
But in chess terms "Middling player occasionally made suspiciously good moves" is a pretty weak cheat report. But if you can tell they had stockfish running and changed windows to it several times in the course of the game? Well, now you've got a very clear cheat report.
More broadly, many gamers are chasing the dopamine rush of winning, complete with slot-machine-style flashing lights, music and dancing character animations. Being awarded a win by e-mail a day or two later doesn't really compare.
What if the cheater is just running stockfish on a separate laptop, is the anti-cheat system also going to turn on the webcam and track eye movement?
> Being awarded a win by e-mail a day
That is only half of the story. The other half would be in banning the cheater and making them lose access to their account, i.e, impute a real monetary cost to being caught cheating. Make it expensive for those caught cheating and equally expensive for those making false reports and I'd venture that we would see some sort of equilibrium where cheating is not worth it.
The cost can (should) be progressive for repeated offenses, and it can be divided if multiple people make the same (wrong) call. Say you get one "free" report per month, but you don't lose it if either you were correct and/or more than 5 people reported the same person.
The important thing is not about being "perfectly provably fair", it is just to curb abuse (on either side) so that people still can have fun playing without having to accept such invasive software on their machines.
But in chess terms "Middling player occasionally made suspiciously good moves" is a pretty weak cheat report. But if you can tell they had stockfish running and changed windows to it several times in the course of the game? Well, now you've got a very clear cheat report.
More broadly, many gamers are chasing the dopamine rush of winning, complete with slot-machine-style flashing lights, music and dancing character animations. Being awarded a win by e-mail a day or two later doesn't really compare.