If I was in charge, I'd certainly go that way. I'd hire a young, up and coming HC, and stick with him through thick and thin. Get back to how this franchise was orginally founded: GM - Player Personnel - Head Coach. Three different people who can work together but would not step on the other's role.
Since I'm not in charge and the Jerrathor is, here's why I disagree with your premise somewhat.
He needs that stadium filled at least through the next two years before he can begrudgedinly admit we're going to start rebuilding. Bringing in a new guy is not going to turn this particular team around because it's best players are at a career stage where they're not young guys anymore ( they're not old either ) therefor, they're not going to be as " open minded " as they were when Tuna started all of this. In other words, the fear of losing their jobs is gone.
Once again, I believe the Jerrathor is going to bite his tongue and give up some power in order to bring a vet coach who could bring back the disciplined that has been eroding since Tuna left. I'm not saying bring Tuna back, that bridge has already been burned and even if he wanted to coach again ( which he doesn't ) his threats would fall on deaf ears. Somebody like Cowher ( who should be the first choice ) or even Holmgren, signed to a 3 - 5 years contract at roughly 7 - 10 millions with SOME personnel power. Somebody who has enough sand in their saddle bags to get in this players faces when they make stupid penalties. Somebody who will toughen this bunch up, mentally and physically. Starting with the QB. Even if most of the tough guy act it's just perception and not reality.
Jerrathor has way too much money invested on that stadium, and this team for that matter, to turn it over to an inexperienced guy. He needs the name AND reputation.