Sorry if I misunderstood but that is how I look at a QB picking a coach, that would be picking his boss.
It's not about the QB picking his coach. It's about him having some input.
Example: The Lakers didn't hire Frank Vogel because Lebron wanted him. If they hired who Lebron wanted, Lue would be coaching them.
But, you can be damn certain that they made sure Lebron was okay with it before they hired him.
When I was having my assistant and/or a key employee sitting in on an interview, it wasn't so that they could pick who they would work with/for. It was because giving them a voice made them more invested in the company and in what we were trying to accomplish.