I just... why?
"A user who gets through all of this would end up either with a PS4 running Gentoo on the 4.4 kernel, or (more likely for most users) a bricked machine."
So, you go out, spend the money on a games console that can already do stuff like access the net, and then you either turn it into a malfunctioning lump, or put an OS on it that would have been more useful on a cheap, modularly upgradable PC that would cost the same amount or less. Other than bragging rights and epeen, I really and honestly fail to see what is to be gained by doing this. If it actually made it more useful, sure... but go back to the part about the PC being cheaper, upgradable etc.
Frankly, if you penguins are wanting to do something unusual, write a proper replacement browser for my N900 and its aging MicroB. Now THAT would be useful!