I know you directed this at Box Ray, but I can't resist. Where do you think coaches and coordinators emerge from...coaching is a fraternity and most successful coaches are the fruit of select, elite coaching trees.
Bill trained RAC who was never more than a position coach in his years with the Giants and JETS. He was passed over many times including by Parcell's when Bill wasn't available. Charlie was a HS coach when he joined the Giants as an assistant working on ST (under BB). He had worked his way up to position coach when Parcells came here. After Parcell's departed for NY he was named the OC of the JETS, although Parcell's emasculated him as a playcaller before he left to follow Bill to NE. Charlie was running Ray Perkins Giants offense he learned as an assistant working his way up through the ranks. It's the same way any coordinator learns to be one. You tweek it depending on personnel and goals (generally your HC's...) and successful creative capacity.
Belichick has a system and scheme on both sides of the ball he developed or developed an affinity for and apprecaition of over years based on his Giants days. He will either hire guys who knew it like RAC and Charlie, or guys who are bright enough and committed enough to learn it or who were exposed to it by former protoges. He won't ever hire someone with name recognition because of their limited success or abject failure elsewhere to come in here and install a system they were taught somewhere else or developed based on where they came up in the league. Only HC's who don't have their own system or the x's and o's capacity to adopt or develop one assemble a staff that can generate one on one side of the ball or the other and occasionally both. When things don't work out for those HC's, the coordinators are the first thing to go. More often than not, eventually the HC's go.
Part of the reason Kraft hired BB was because he came with a system and philosophy that an organization can ideally sustain even when he decides to call it a day as a HC. He taught/teaches those who teach the next generation. If Dimitroff and Pioli and McDaniels are successful running the system they may find the master poaching their staffs before all is said and done, and one of them may even return to run it here when Bill is ready to hand over the reins.
Beats the hell out of swapping failed flavors of the month coordinators and eventually HC's every couple of seasons when things don't work out...like in Buffalo or NY. That's why Miami hired Parcell's, to build infrastructure and install a system and build a team that can compete. Ditto KC and Atlanta and Denver. Spoiled fans demand championships. What most owners want is competitive consistency.