This was pretty much my take too. I'm not in the game industry, but it seems to me there are plenty of generalists. Only they don't work on these massive AAA titles, but on smaller titles in smaller teams, or even on their own, because that's where you really need generalists, and where they are appreciated. The large projects always sound so corporate, structured, and compartimentalised, that it doesn't sound like there's room for generalists.
I think it's simply a choice made by these big title publishers. If you want more generalists, give them more freedom, more leading roles.
Mind you, I don't work in the industry, so I could easily be wrong, but this is my impression as an outsider.