It's not that simple.
It's do you want to have a complete overhaul of your organization ? Do you want to adopt his culture? Do you want to do all that he wants for a short term rental? Because in 3 years max, he's going fishing in Nantucket. If you're a GM or a team president, do you want to work for Bill? Does Bill want to only answer to the owner? If so, the GM and President are hiring a boss, one that is not the team owner and one that's not going to be here for long.
The other layer is : Does Bill still have it. Tom Brady left and, clearly, he'd had enough of Bill. His team went backwards the last 3 years. More importantly, Robert Kraft didn't want Bill anymore. If I am an owner, I take that into consideration big time.
Coach? Sure. GM? Probably not.