Don't really feel like debating the whole Bill vs. Brady thing all over again, but one of the ingredients for SB winners has been having a Top 5 or Top 10 defense. Of the 57 SB winners, 33 of the 57 (58%) had a Top 5 defense in terms of points allowed and 47 of 57 (82%) had a Top 10 defense in terms of points allowed. This year, if BAL (1 in fewest points allowed), KC (2), or SF (3) win the title, another team with a Top 5 defense will get added to the list.
There's no arguing that 1) Brady made a huge impact for years, 2) he saved the offense his last few years in NE, 3) that the Pats couldn't overcome not having him there since he left and the offense turned into a mess, 4) that Tom didn't play defense, and 5) that BB consistently produced top defensive units. In the 6 titles for NE, the defense ranked 7th, 1st, 8th, 2nd, 1st, and 6th in points allowed (the years the Giants won with BB as DC they ranked 1st and 2nd).
There have been plenty of teams that had HOF QBs and high scoring offenses. None of those teams won 6 titles. While the game is different know and the game has evolved, it still takes a team with a good defense to win. Granted, it also takes a good offense to win as well, but it's pretty rare for teams with great offenses and below average defenses to win (2011 NYG 25th in PA, 2009 NOS 20th in PA, 2006 IND 23rd in PA were the only ones ranked in the 20s).
I still think the mindset of having a very strong defense paired with an elite / HOF QB is a great strategy to win. The problem for BB and NE was that once TB12 left, they did not have a HOF QB to make that plan work. BB the GM hasn't been great for years, but IMO, if Bill coached BUF, KC, or DAL, then he could still win a lot of games.
I think, in general, you are very accurate with this assessment. The issue I am having, when analyzing the greatest run in NFL history, is a full realization of how bad Brady's weapons were. All year we have heard about the bare cupboard in KC, but look at the history of New England's drafts and find the rookie receiver that is as good as Rashee Rice. Rice is an investment in Mahomes' success that is paying off. Kelce is a gronk level weapon. MVS, Hardman, and Moore aren't great, but how do they compare to reche caldwell, david patten, danny amendola, chris hogan, and many other journeymen that Brady made into weapons? So the rub for me is that Brady couldn't have had the same success without Bill the DC and that defense, but he was also really fighting uphill on offense, due to some pretty terrible management by Bill the GM. That extra level of difficulty can (and should) serve to elevate our perception of Brady's greatness, but I don't know that it takes away from Belichick's coaching greatness as much as it indicates a professional blindspot (personnel management) that eventually caught up to him. Brady may have fooled Belichick into thinking he was pretty good at doing everything, soup to nuts. Take away Brady and you still have the greatest defensive mind and gameday schemers in NFL history, but that isn't enough to overcome bad personnel.
BB the GM relied on TB the HOF QB many times to make do with some mediocre weapons and lower priced offensive players. In the salary cap era, BB helped form the strategy of spending less on a QB and surrounding offensive weapons to have more cap dollars to spend elsewhere. That worked for almost 20 years and achieved sustained results and success that no other franchise has seen in the salary cap era.
Brady didn't win a title in 10 years across what would be considered the prime years for most QB (28-37 years old). Those were the years where Brady did get upgrades in weapons, yet NE DIDN'T win. Some guys were there longer than others, but guys that came and went included Moss, Welker, Stallworth, Gaffney, Maroney, Gronk in his early years, Hernandez, Branch Part 2, Ocho Cinco, Lloyd, and others). The Pats had multiple seasons scoring 500+ points, but the defense wasn't as good in some of those seasons (whether that be by inferior personnel, more $$$ spent on offense, bad luck in the postseason, etc.) That just illustrates how difficult it is to win in any given season.
BB and NE found that the spend-less-on-offense strategy only works with a HOF QB. Mac Jones couldn't win without more pieces on offense (and a lot better pieces at that). I don't think that means the game has passed Bill by, I just think that means he can't win going cheap on offense without one of the best QBs to ever play the game. I would guess that if he went to a talented, already built roster, we'd see that Bill could still coach and be successful . . . but just don't ask him to lead a rebuild.