Coaching certainly matters a lot in the NFL but I would rank it third in importance behind QB and GM/Player personnel.
Even the best Head Coaches will not succeed without the right players. We're seeing that in NE now. I don't think there's any doubt that BB is a great Head Coach but he's a below average player personnel evaluator and was bailed out because he had the GOAT at QB for most of his career.
That last section is a bit of an over generalization. For starters, I think for NE's first three titles, Brady was bailed out by a GOAT coach and team builder and was mostly a passenger. BB took a bunch of retreads, made some great draft picks, and established an elite defense. The Pats won early on due to a great defense and a strong running game, with some timely contributions from Brady. He was a judicious game manager that made some big plays on occasion, but they needed him mostly to not turn the ball over. But Brady was not the primary reason NE was winning in those early years,
In the 10 years in the middle, Brady carried the team and NE tried a lot harder to turn the offense into a super power. In what should have been Brady's prime years, NE didn't win. That's one of the oddest things about the NE / BB / TB story. They invested a lot on the offensive side of the ball, but that wasn't enough. A number of years the defense suffered because of it. By the second NE run, there's no doubt that Brady was the main cog on the team, but BB had done plenty to have pieces around Brady to help him succeed. But BB's game plan won them their last SB against LAR. The offense did hardly anything, and the defense totally derailed the high flying Rams offense (for the second time in the SB).
BB "the below average player personnel evaluator" drafted / brought in / coached multiple current and future HOFers, turned no names and retreads into All Pro and Pro Bowl level players, and has been the single greatest salary cap manager in the 27 years of the salary cap. None of that is really opinion, as all of those things are essentially facts.
If people want to suggest that Brady was first on the list of the things that made NE great and the biggest piece in a near 20-year run of success, I have no problem with that. But the list of all the things that made NE great is pretty long, and Brady can't stake claim to all the other reasons. If folks want to say that BB is not at good at picking players or signing free agents that fit in the current state of the NFL, I have no problem with that either. But to suggest that's always been seems off base.
NE under BB drafted Brady, Seymour, Light, Branch, Samuel, Wilfork, Mankins, Gostkowski, Mayo, McCourty, Gronk, Hernandez, Chandler Jones, Hightower, etc. He took guys they had and made them better players (Law, Bruschi, McGinnest, Faulk, Vinatieri, Vrabel). He added big pieces without giving up much (Dillon, Moss, Welker, Revis, Talib). Sure, Brady was the main attraction, but NE wasn't winning titles without a long list of other big contributors. Yes, Brady "bailed out" the team many times, but the coaching, the roster, the defense, and many players bailed out Brady on a regular basis, too.