Yeah, I don't see England taking a foreign manager. Especially in the post-Brexit era. And doubly so for a German.
Point blank, there hasn't been the promised Klinsmann tactical revolution in the United States. I'm not as negative on him as I used to be (I think he got the tactics and squad selection as correct as he could have for the Copa), but I don't think he's the best fit for us, either.
That's not necessarily all Klinsmann's fault. We're going through a bit of a lost generation at the moment, and the development system over here is [Poor language removed], to say the least. MLS has a lot of control over this and has many bad motives, for one thing. The system as a whole is too fragmented for US Soccer to control. It would require a lot of two bit soccer "lords" buying in and marshaling their tiny little fiefdoms to make real progress.
And that's not to say he couldn't do a German-style revolution with England, but they have their own set of bureaucratic challenges that Germany doesn't seem to have.
tl;dr You're right, England probably need one of their own to convince the FA and everybody to go along with the necessary changes. Just as the US at the end of the day needs a seasoned MLS coach to tell the league to cut their crap, not an outsider. Y'know, the same sort of figure Klinsmann was for Germany.