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They'd have issues with their DRM doing that. They should ship the Steam binaries properly through apt and yum repositories, but I doubt that they'll ever ship the games that way.
I don't see why. If the Steam-DRM'd version of a game requires Steam installed in order to play, they can just add the Steam package as a dependency. Possibly a bigger issue would be that Steam has incremental updates (fixing a bug in a game requires downloading a fixed binary but not the multi-gigabyte data files) while most Linux package managers do not support incremental updates (when Debian releases a new LibreO…
I think it makes sense for Steam to be isolated from the rest of the system as much as possible.
It is also helpful to Valve if it is as consistent with Steam on other platforms as possible.
Game downloads can be pretty big and take a while too, I'd rather not have apt locked for an hour while it grabs some large game update.