Belichick has 6 Super Bowl rings with the GOAT QB so I would hope we're not leading off his bio with "impressively" winning 7 games with the corpse of Cam Newton.
NYJ had a couple seasons under Rex Ryan when the defenses were stout and the offenses would have been plenty good enough with Brady to at least make it to a Super Bowl. Similarly the Jags had a couple of seasons with great defenses and an elite quarterback away from contending for a Super Bowl. Also, I'm betting a couple of seasons with Brady and Calvin Johnson, Golden Tate and Reggie Bush would have been highly successful and entertaining. You plug Belichick into those situations with Sanchez, Bortles and Stafford, and I don't think they're improving much. Just my opinion.
Overall I agree with the 'ultimate team sport' idea however I also think quarterback is the most important position in all of team sports, which along with Brady being the best ever at the position, is why I personally give him more credit than Belichick for the success of the franchise. Brady also has very nicely capped off his narrative by winning another Super Bowl with a second franchise.
SB's 36 and 53 are the most obvious examples of good game-planning and defensive execution combined with late-game clutch quarterbacking (i.e. ultimate team wins). SB 39 falls into the ultimate team win category as well. I'm giving the other 3 Super Bowls to Brady.
I'm not putting them in the 'legitimate SB contender' category until I see what Mac Jones looks like next season. It's not just a Bills / Josh Allen problem either, the AFC is loaded with very good teams with very good or better quarterbacks.... Bills/Allen, Chiefs/Mahomes, Bengals/Burrow, Chargers/Herbert, Texans/Watson. All of those teams (except for the Texans who Watson may not be playing for anyway) have better supporting casts around their quarterbacks as well so Mac Jones needs to improve and his supporting cast needs to improve A LOT. I don't think it's a given that either or both of those things are going to happen.