I think it's clear that one of the reasons the Patriots are able to cheat so frequently and effectively is because of this sort of attention to detail.
However, it may also be the reason Pats coaches that move on to other teams tend to not be as successful. Diagramming plays for critique is a great learning tool, but a very narrow learning process. In particular, if it's bottle-necked through Belichick, as you describe it, he's creating a sense of dependency in coaches on himself, and denying other coaches the opportunity to learn how to teach the way he does.