I don't think we know this about BB at all. I tend to agree that BB would want total control if he's going to take another HC gig, although if no team will give him that and he really wants to catch Shula that might change.BB is not taking a booth or behind the scenes job and any suggestion that he'd want less than he had for the last 2 decades is wishcasting in the hopes of seeing him remain in the game. His decline of the 49ers opportunity is completely consistent with everything we know about BB and what he probably wants.
But it wouldn't have surprised me if he did some kind of consulting or behind the scenes work for a team, just to stay in the game but without the rigor of being an actual full time coach. In fact if you told me he wasn't going to be a HC in 2024 I would have bet on him doing something like that as opposed to a media job.