Attestation could help, but I'm not sure if it goes in the spirit of what Valve tries to do with their OS. The system is open and you can easily access the desktop (it's a first party feature) and thus do what you want. Maybe with a separate verified boot state without desktop but the user experience would not be great.
And in the end, like you said, they'd run to only support sealed attested systems if they could. But cheats have evolved past being run on the computer running the game. Some use DMA or are in between the keyboard/mouse and the usb port. Consoles also have their fair share of cheaters. None of those would be solved by attestation.
Valve has shown recently that it's possible to fight cheaters without kernel AC or attestation. It's just a bit more difficult and intensive so other AC providers won't go the same route.
On windows with kernel anti cheat you would need to find some vulnerable driver, sign your own driver, or use external cheats like DMA or vision based. This funnels cheat devs into using a few methods that anti cheat devs can focus on for detection. Is it perfect? Clearly not as there's plenty of cheaters anyway. But its much more effective than what these anti cheats can do on linux.
