I'll posit that it's because most of the "big websites" started out small. Google, youtube, facebookYoutube, Facebook et al. were all at one time single-server sites that someone built as a hobby. They used LAMP-like stacks because: 1) they're cheap and the devs were poor and often 2) because they were at a university and university environments tend to favor OSSOSS.
After the sites started growing, the developers just stuck to what they knew. In the early years, there wouldn't be enough time or money to do a big system rewrite. When, and if, that ever became an option, why switch to an entirely different base?
So I'm saying it's because that's just what they knew and had when they started. SO isn't any different if I recall that story correctly. The SO Founders knew MS stack, and had access to the tools/liscenseslicenses/etc to start using it, and so that's what they used!
(I've also heard that they also wanted to prove that MS stack was just as good as LAMPLAMP for big sites, but that may be apocryphal.)