If memory serves, when Valve was initially getting their feet wet, publicly, with Linux, they were getting Left 4 Dead (1 or 2, can't remember) to work there. If I remember correctly, they got it to a point that hardware for hardware, they got the Linux port to run better than the Windows version.
And that's a direction worth going if you want the gaming crowd to follow: come this way and get an extra boost in performance. We know you just spent $300 to get a couple frames per second boost, come get a few more for free.
They really need to do something about Big Picture mode though: that thing looks terrible on anything above 1080p. Even more so at 3440x1440 where it is blurry and inside black bars. If they're trying to make Steam into an appliance of sorts, the user interface needs to be right.