Does it? When Phillips was HC he asked to increase fines to get players to show up on time and Booger said no and even said some had "media passes" to be late. Later that season, the team came apart and Phillips caught the flak, that should have been laid at Booger's doorstep, he not only invited that, he helped create it. Johnson called it a country club atmosphere for a good reason.
One of Parcells first acts was to take control of his locker room. Emmitt bucked him and he cut him. That doesn't happen without total coaching control. The last thing a HC needs is the owner in any player's corner.
When Kraft got Belichick and Brady to reach that compromise, he did make sure Brady gave up something in return for Jimmy G getting traded, about 10M a year at the time. He could have just told Belichick Brady was the guy but then Belichick wouldn't have been.