ken, this is like four posts in one.
I'll to respond to your thoughts on my favorite subject... what make BB so successful? There's nothing in what you've written that I disagree with in the least. I would just choose to bunch and group the concepts differently. The "Belichick" recipe will be a matter for football historians to dissect for decades... so we may as well start the ball rolling.
1. Versatility
In scheme, to be adaptive to game situations... which extends then to searching for versatility in the skills of the players he drafts. Part of what makes Gronk so effective is that he is a legitimate dual threat as a blocker and a receiver; outstanding at both. Players like Hightower than can play inside, outside, rush or drop into coverage.
The fact that the defensive scheme can switch from a 3-4 front to a 4-3 front from play to play (they did this against Buffalo and against Dallas this year) is amazing. Consider the fact that most teams have to commit their organization to one scheme, and if they ever want to swap it takes them years to retool their roster to find players who can run that front. Belichick's team swaps their defensive front from snap to snap.
2. Study and Mastery
You call it coachability, and it has also been called "football smarts" and "student of the game". But I'll put another spin on it. There are players out there who study their craft meticulously, and latch onto teachers who can evaluate every muscle twitch and make corrections. Brady is an example, an aging veteran, still improving and adding to his game: mobility, throwing motion, diet. He's obsessive. Edelman talks about the pride he takes in mastering the nuances of punt return, to squeeze every bit of opportunity. Chandler Jones has been in the press with comments recently about how the game is slowing down and he can see how the offense is going to attack him, and how we can counter it. These are players who don't rely on pure raw talent, they work at it, they study it, they sacrifice in other areas of their lives to obsessive on getting their hand placement just right. When BB talks about "Do Your Job" and do it well, he's talking about focus and commitment and study.
3. Depth over Flash
Belichick is famous for jettisoning his stars, including the players that he turned into stars. He philosophically chooses abundance of talent on his roster, over elite talent, when he has to pick. If he can afford to keep a Gronk, a Seymour, a Wilfork, a Revis, a Mankins, a Milloy, a Welker, a Vinatieri... then he will. But he is conservative in the valuations he assigns to any one player, and will underbid for star talent to save cap space for the likes of Sealver Siliga, Jonathan Freeney, Josh Kline and Marcus Cannon. And if releasing a veteran at the peak of his game leaves a gap on his roster, he is confident that the team can compensate for it in scheme, by dusting off a JAG or asking a UDFA to step into the spot.
This makes his teams incredibly resilient to inevitable injuries, and keeps the franchise competitive regardless of who is lost to the IR. Dallas has been crippled this year by the loss of their star QB, their star WR, key players on D. Belichick has a plan for every spot on the depth chart, three and four players deep. The Pats were prepared to go into 2015 with Garropolo as their starter, and I bet he would have been focused, poised and competitive. Any other GM would have decided "Brady or Bust" and signed a guy to hold the clipboard and take some garbage snaps. BB spent a 2nd round pick to give the roster quality depth behind the GOAT.
The expression of "Depth over Flash" is also clear in the draft, where BB will habitually trade down to collect more middle and late round picks, many of which don't make it past Training Camp. He invests franchise assets to find quality at #3 CBs, #4 OG, #4 TE, #6 DT. And this is clearly the priority over Wes Welker, Logan Mankins, and innumerable other franchise players that have passed through BB's hands. He is constantly kicking the tires on no-name players, cast offs, panning for gold. When he finds Benjarvis Green Ellis, Stephen Neal, Deon Lewis and Malcom Butler, people think it's just dumb luck.
4. Preparation and No Excuses
The Pats train their players for situations that no one would ever imagine happening. And then they happen, and the Pats are prepared for it. What other team would practice how to defend against the Swinging Gate fake punt, and be less surprised and more prepared to execute than the Colts team that chose to run it? That game when the Pats long snapped the ball out of their endzone to concede the safety, so they could change field position... who else would have practiced that play beforehand.
The last Foxboro home game loss to the Dolphins was the game in which the unveiled the Wildcat. After the game, there was no sad talk about "deception" and "unfair play", requests to implement new rules or a new point of emphasis. Instead, the Pats studied up, practiced how to stop it, and the Wildcat never burned them again.
Jonas Gray overslept? Brandon Spikes got into a car accident and left the scene? You have to focus on the things that you can control, and there are no excuses. The solution for disorientation is preparation.
In the draft, the expression of this is detailed, independent scouting. The Patriots interview players who they have no reason to think will ever fall to them, and who they have no reason to draft. And when they draft Jamie Collins, and everyone says "WHO?!?!?", all of Patriot's Nation has learned to say "In Belichick We Trust". His unambiguous intent is informed by exhaustive study and preparation, and only years later do people really see the genius and thoughtfulness that went into the evaluation.