Why? Because there's no publicly apparent hierarchy? The players know who they answer to and who calls plays. If you're arguing that the coaches suck, that's one thing; but you're arguing that the mere lack of a formal title affects their ability to coach. Are you suggesting that players are not listening to O'Brien and Patricia? You seem to think these guys lack the experience and chops to coach NFL players, so I'm not sure how naming them as coordinators would affect that evaluation. Are Darius Butler and Pat Chung going to wake up tomorrow to the newly minted Matt Patricia - who, by your implication, isn't likely to command the respect of NFL players readily - and decide he's a smart guy who should be humored? Bullshit. They're given a LOT of responsibility by Belichick, and the players see that. Whether they listen to them or not has nothing to do with their title - since their positions are clear in practice - and everything to do with their personal perception of the coach's knowledge and effectiveness.
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.
And don't use Thomas as a representative example of anything. He didn't act out because of Matt Patricia or his lack of control; he acted out because he was pissed off at Belichick. His 'torpedoing' of the locker room was in no way related to a lack of respect for the defensive staff; it was all directed at Belichick. What was Patricia going to do; would Romeo Crennel have found a way of dissuading Thomas from stamping his feet? I doubt it. This is shitty analysis, and you know it.
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?
Anyway: are you arguing that Belichick is deliberately assembling a shitty staff - granting you this arguable premise - to serve his own vanity or out of some ignorant faith in his own abilities?
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?"
EDIT - Yammer, after reading your posts again, it's pretty clear to me that you're critical of Belichick's staff decisions generally and are using TMQ's haphazard criteria to express it. Just come out and say that you think Pepper Johnson should be the DC or that O'Brien and Patricia have meager resumes. There's no earthly way you really believe the controlling factor in the players' opinions is the title on these guys' doors. They fulfill the same duties as other coordinators, which gives them de facto authority. Honestly, if players are consciously ignoring them or distrusting their judgement, it's not going to be fixed by naming them Supreme Overlord of DCs.
See what I wrote above. Oh, and get the sand out princess.