Maybe Jon Gruden ends up being Saints HC?

You say that, but once Tom Brady left New England fell apart under Belichick. They weren't one franchise QB away from being great by the time he left.

Being an NFL head coach is an incredibly difficult and demanding job. These guys basically have no life outside of football and it's why so many of them end up divorced. And the burn out rate is really high. Belichick for example, as great as he was, really just looks like he is done and burned out.

And frankly Gruden was never a great coach. He caught fire for a couple of years but the league caught up to him and he left the game for 10 years because he was burn out. And frankly, when he came back he wasn't a good coach. Again, he had a 22-31 record in his second stint with the Raiders. There is no reason to believe he is going to improve on that.

If there was a HC candidate out there with experience that had not proven to not be a good HC by getting fired, then sure hire him. But at this point they need to look for new blood that will bring new ideas. I'd consider Ben Johnson, Slowik, Aaron Glenn, and Rizzi off the top of my head. And I'm sure it wouldn't take long to find several other very qualified candidates for the job.
Bill is 72 and is likely done. Even after TB14 left, when teams played NE, they knew they had to prepare against a well coached team. The problem is, is that you need an elite Qb. Then once you have the elite Qb, you have to build around him. Starting with the Oline and playmakers. Bill is a defensive minded HC, so you'd know the D would be solid. The problem with the guys you mention will have to succeed immediately or else the fans will turn on them immediately. Because theyve never done it before. If we were already a top notch deep team with decent salarly cap to work with, then youtake your chances on a young guy. But we're staring down the barrel of 3-4 years. And no young coach will survive that. (dont forget that the players that make this team relevant are all of the older guys, and they will all have to be replaced)