If it's running SteamOS (and it will be, even if there's Windows compatibility Valve probably doesn't want to pay for licenses), it might as well be locked to Steam for 90% of people. Epic's launcher doesn't have a Linux version (since they've claimed as have many other developers that the Linux community is 1% of users and 90% of complaints due to distro differences), nor does EA, Ubisoft, etc. They could port it, but by time they had something user friendly and working (which may be difficult since you probably won't get more than Steam Big Picture which doesn't have support for installing non-Steam applications at the moment) Valve would've sold a boatload of these and a bunch of Steam games.

Edit: not to mention anti-cheat, which is a whole other kettle of fish when you have to integrate into a entirely other kernel with different plumbing. Valve's anti-cheat doesn't rely on kernel modules or a ton of client side software at all, so they have a cross-platform advantage there too.