You skipped over my response to this (a similar post) this when I responded a few weeks ago.
The offense in 2001 and 2003 were "asked to be efficient" despite lacking the tools that would normally allow them to be efficient. Of course the defense is the better unit since all of the best players, big contracts, and draft picks are on that side of the ball. During that era, there were plenty of good defenses that were still bad teams because their offense sucked,. Having a really good, playmaking defense, during that era, wasn't like having a rare diamond as it is today.
In 2000/2001, the offense was a bottom-of-the-barrell unit with no notable offensive linemen (zero pro bowl players), Troy Brown as their #1 receiver, David Patten, Antowain Smith, Patrick Pass, Christian Fauria, etc. Asking them to be "efficient" or even average would seem to be a lot to ask, which is why they were horrible with Bledsoe as the QB. It turns out, in hindsight, in looking at all of the players, coaches, etc. and what they proved later, is that this was not just a really smart chess game with incredible coaching, Charlie Weis's next level gameplanning, etc. It was almost entirely because Tom Brady came in and carried a really subpar cast of players. And the offense was pretty good, above average, after Brady took over. 14-3 after Brady took over; 5-13 prior to that.
In 2003, the offense did have Branch and Givens, two good (but certainly not superstar) receivers but had a running game averaging 3.4 yards per carry, easily the worst among the league's better overall offenses. The Patriots still finished as one of the best performing offenses overall (points to turnovers) despite having maybe an average receiving corps and a very bad running game. Again, this should not have been an efficient unit that could score when it needed to; 17-2 with that offense should be nearly impossible in any era, but for Brady carrying them.
I give Bill credit for the 2001 and 2003 Super Bowls, but that doesn't change that your take is full of holes. You once again point to the overall performance of the offense and overall performance of the defense. What you leave out (again) is that Brady was still by far the most valuable player on the team and was dragging subpar players, while the defense was studded with talent and contracts. That is what defines a lot of the relationshiop between Brady/BB, and I'm not saying it's a bad thing. BB managed the roster correctly; that doesn't change that Brady was a massive outlier in being capable of making a terrible supporting cast "efficient."