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.
Secure Boot in theory isn't even necessary, only TPM2. Secure boot only ensure that you are actually booting into a binary that you expect to boot in this case, so if your binary is actually different it would result in different PCR values in the TPM indicating something is wrong.
Sadly a lot of end user software (flatpak, ...) isn't packaged & signed in a way which would allow for full "only run software I allow by importing public keys" (read Linux IPE[2]), but what can you do, only your best I suppose...
[1]: https://www.freedesktop.org/software/systemd/man/systemd-sys...
Those things are all possible, but really the only entity that has the power to realistically do them is the OEM - Valve could do it for SteamOS, but only on it's own hardware.
Given that a certain amount of windows gamers have been having issues making sure their PCs complied with the config requirements for the latest COD/Battlefield, it would seem an even higher bar for a consumer targeted bit of software that needs to do more to be running securely (or add a different mode to your distro install and reboot to it), alongside the wider variety of distros/configs. Distros advertising themselves for gaming or getting people to migrate from windows are also trying to keep barriers to entry low or to appear simple.