Given that there are a number of instances of NFL players simply tuning out coaches and deciding that they don't have to answer to them, I have a bit of a leg to stand on with this concern. Your statement that "they are given a lot of responsibility by Belichick and the players see that" is a sentence that reflects your desire. It may be true, but you really have no inisight into that. You want that to be the case so you write it. There is a data point - last year Dean Pees lost control of his defense, driven by a guy who played directly under Patricia. Does that make Patricia unable to control his men? Not necessarily, but it puts a small red flag there. He certainly doesn't command the respect that a Pepper Johnson or a Dante Scarnecchia does, and if the team has a 2-3 game stretch where the team has a hard time putting things together then are Patricia and O'Brien able to keep the locker room? They may well be, but not giving them a badge sure seems like a risk.
Let's put it this way, if it were a great idea not to name coordinators how come teams put in interim coordinators and then hire someone as a coordinator so quickly? In the military it is a concept known as clear chain of command, and it is considered pretty damned important.
I don't at all know that, and your hypothesis that he was angry only at Belichick is again, what you want to believe about a situation into which you have zero insight. I guess I could buy that a guy who grew up in the game being coached by very sharp defensive minds throughout his career (and in college too) could be irritated with a position coach and a coordinator that he felt was not providing him with the best opportunities and the best guidance. Why is that a leap?
I don't think he is assembling a sh*tty staff. I think he promotes from within the same way Parcells ran his system and, for the most part, the results have been pretty good. But not giving them the coordinator titles is a very curious move as it risks blurring the chain of command. If Bill Belichick told me last season that I am playing the Joker role in the Okie defensive set, so I am attacking the QB, and now Patricia is telling me that in the Okie I am playing a run stopping role from the same spot on the field......if I think I should be attacking the QB am I going to listen to Patricia or am I going to go around him for clarification to Belichick? Or ask Pepper Johnson who has been around the Belichick defense for about 25 years now? It takes away from Patricia's ability to, every now and again, just say "I am the f*cking coordinator, do it my way, OK?"
See what I wrote above. Oh, and get the sand out princess.