I don't think you give a guy like Shanahan full control. I don't think you give any coach full control. The only guy I would consider giving significant control to is Jim Harbaugh. With the other coaches, I'd want a balance of power.
If I really wanted a coach, I'd offer:
1. Final say over the 53 man roster and practice squad (but not the draft and free agency)
2. The ability to choose the GM (within reason)
3. Full control over his staff and the coaching aspects of the team
Yeah Shanahan would never get that full control. He's been blackballed sort of by talkin smack about Snyder, and isn't in a position to drive that sort of agreement as he doesn't have the clout. Dude would not push for that, he'd come aboard in a heartbeat under a GM of that I have no doubt. And that is also why I think the Rams will like him, sad to say, that plus him being a vet coach with tons of experience to include Super Bowl victories.
Harbaugh, yeah, no doubt. You would have zero chance of getting him without giving him control.
The coordinator types aren't going to get control unless a couple teams get into a bidding war for one of them and even then it's an extreme longshot. And that type of situation is unlikely when you have multiple bright young OCs who will be interviewing.
As to the control you mention, the HC typically owns his staff and we wouldn't get anyone good without that, so it's a given for the types we want. Roster, yeah, that's another area where a top coach is going to expect it even a top coordinator that you want.
The GM thing is something I'd work with the new coaching hire in tandem on. No way I'd promise him anything there.
The big one is the draft and FA. And no I wouldn't give that up unless I was convinced he was the right guy and I knew that I'd hire and fire as many complementary GMs as I needed to in order to support him. Only guy right now who meets that criteria for me is Harbaugh, where it would be a similar setup to what we had with Fish but just with a better coach.