I wonder if maybe Bill is the kind of coach that can make a good team very good and a very good team great, but has the opposite problem with an average team -- his methods make them worse.
To me, maximizing the potential of a good or great team is the single most difficult thing for coaches to do in the NFL. Far too often, we see them fuck up. Belichick's entire M.O. seems to maximize greatness. Getting the last few percent to help will his teams across the finish line.
I used to teach SAT prep. (At the time, the scale was 0 to 800.) For the kids who came in testing around 750-760, the idea was to try to get them another 10 or 20 points. For the kids who came in testing at 400, you could get them to 550 or even higher. The thing was that the company very much segregated the teachers -- some of us were there for the 750s and some for the 400s, and you never tried to do both, because they were extremely different skills. I think the things that makes Bill able to get 770 out of the 750s is counterproductive for the 400s. Negative, even. If that makes sense.
I have many thoughts about why I think this about Bill, but it really doesn't matter. The issue for me, when talking about getting rid of Bill, is that I think he does well the very hardest thing to do in NFL coaching. But, unfortunately, he just doesn't have a team that allows him to do that thing. So, it would feel really tough to get rid of him, because I know that he can coach up good/great. And the value to that is difficult to measure and wins championships. The problem is that he may not be the right guy to get back to good/great, and that sucks.