I think the Al Davis-Lane Kiffin-Rob Ryan relationship showed why you let a coach bring in his people. You bring in people to complement your strategy or compensate for a weak point in your style. How do you think an OC or DC is going to feel if weeks after they are hired a coach is brought in that is going to call the plays? It's backwards any way you look at it, the team starts with the coach, everything needs to them complement that. All the offensive and defensive philosophies... Davis might bring in a 3-4 DC, pair him with a 4-3 defensive minded coach while you have a 46 type of personnel group. Without knowing what the HC is going to bring to the table, I don't see how you can properly hire the rest of the staff under almost any circumstances..
But according to who? Have you ever been a head football coach? I like the idea of uou have all your coaches lined up and then you hire your HD according to what has been already been hired to lead your specific areas of your team. Hey, it could work...no on has ever done it from what I can remember. NOT gonna knock it because it is not the traditional way of hiring your coaching staff.