I don't think it's a huge mystery from the UNC side of things. No, if you're a Michigan or UGA or Bama, you don't make that move. Too much risk for a blue blood. But I can see why UNC might have swung for the fences on it. Best case scenario, he's successful and elevates your program. Having Belichick there gets eyes on your program. Worst case scenario, he's not successful, but it doesn't really hurt b/c your program wasn't in great shape anyway.
BUT....
I don't know that anyone could have predicted that Belichick simply would not take the job seriously at all. I saw a lot of predictions about why it may not work or probably wouldn't work, but none of those said it would be because he just wasn't going to try. Since the season started, he hasn't given any indication of really caring all that much about it.
I do agree with
@Greer that the gf is a major factor. The situation was always weird because of the age difference, but there was no way of knowing that she was going to be such a presence and factor. Though it became known fairly quickly after he was hired.
So I do agree that it's a mystery what Belichick was thinking in taking the job. Maybe he was just that clueless about how college ball worked and realized after he got into the day-to-day that it wasn't his cup of tea. Given his total disconnect with college football, he would have been wise to surround himself with seasoned college coaches who know the game. Given his knowledge and experience with teaching the game, I think that might have given him a chance to succeed. But you'd still have the crazy gf factor.