A move like this would definitely not win Linux any friends, because as it turns out the Linux Desktop really isn't that great and you'd just be causing a huge headache for a lot of people. The gamers would be annoyed at having to deal with Linux's bullshit, the Linux Destkop community would be annoyed at the huge influx of new users who don't think "try another distro" (especially after the third distro), or "write your own driver, it's open source!", are acceptable solutions to their problems.
If Linux wants gamers there's a simple (note: simple != easy) thing they have to do: make their platform attractive to gamers and game developers. So far they can't manage either, the only reason gaming on Linux is even remotely viable is A) Valve coming in and saying "Ok, since there's no such thing as a standardized base system in Linux Desktop land, here's a standardized base system for Steam you can target", and 2) the popularity of Android making engines like Unity and Unreal have Linux support, which allows devs to tack it on without too much extra effort.