Let's take it case by case.
Mangini. Went to the Jets. Jets were/are a dysfunctional organization that swallowed up coaches before and after him. Then went to Browns. Ditto.
Crennel. Went to the Browns. Ditto. Possibly not HC material anyway but a DC lifer like Wade Phillips?
Weis. Notre Dame. Impossible expectations at that point with organizational obstacles like higher academic standards.
McDaniels. Of all the assistants, I would have thought this would be the hit. The ownership group was stable and proven, unlike any owner that Mangini or Crennel got. It started out well. And he definitely cleared out some deadwood by jettisoning Brandon Marshall and Jay Cutler. His drafts were horrendous, though. He made enemies, and the actual taping scandal gave them an out.
Nick Saban. Had team doctors nix signing Drew Brees due to medical reasons in favor of Duante Culpepper. The end.
ETA: Bill O'Brien! Forgot about him. Bill is a relatively successful head coach who has brought the Texans to the playoffs multiple times. Even if he's fired at the end of this year, his tenure at Houston (and Penn State probably) isn't a failure.
For Mangini and McDaniels especially, they seemed to go overboard with a "my way or the highway" approach as a way to stake authority. But anyone who's actually gotten any in depth into reporting about the Pats coaching methods always seems to realize that Belichick knows when to ease up and put on the breaks. He's not just a hard ass. And he seems to have genuinely respectful relationships with many of the players. "You always know where you stand with Bill" is something I seem to remember hearing a lot, most recently with James Harrison. Players leave and some are bitter about contract disputes or whatever, but very few are bitter about on field stuff. The actual coaching. We hear about that so rarely we could probably list the critics by name. Cassius Marsh, Adalius Thomas.... Maybe kinda sorta Chris Long.
And let's list four assets that Bill has had in his New England tenure that his proteges don't have: Bob Kraft, Dante Scarnecchia, Ernie Adams, and of course Tom Brady. I think having any one of them would be worth a win or two every season.