A trusted entity (probably Valve) could provide a locked down distro where kernel integrity is enforced through secure boot and TPM attestation, but that would mean giving up some control over your own system. There's no guarantee that anything client-side is impossible to bypass of course, but the goal would be to more or less match what Windows offers, which isn't perfect either.

> giving up some control over your own system

There could simply be a developer option that disables these integrity checks but subsequently breaks online games that rely on them. Valve could also offer a module that allows signed user-space binaries access to kernel space, which would be an improvement over Windows offers in that anti-cheat wouldn't need to live in the kernel.

I think that's a fine trade off.

Could reboot into secure mode for these types of games.