I don't really think your characterization of New England's roster building strategy is fair. These players aren't scrubs. They aren't all time greats, either. What they are is smart, versatile players who are capable of adapting to different schemes on the fly and installing completely new offenses with just a week of practice.
This is the real genius of Bill Belichek, imo. His teams are always built in such a way that he can counter whatever his opponent likes to do. The Pats are in no way, shape, or form wedded to a single scheme on either side of the ball.
If they face a team with a strong front 7 they'll just spread the field and throw it 50 times. Belichek laughs at OS's notions that "mixing things up" is necessary to run a successful offense. He's not going to send his RB into a brick wall for the sake of variety.
In the 00s when the Steelers had one of the premier defenses ITL, especially against the run, the Pats would throw 50 times and run about 10-15 or so every time they played them. The hooded one correctly surmised that excessive rushing attempts, especially on early downs, would just be wasted plays.
By the same token if the opponent is a squad with an undersized, passing rushing D-line and a LB corps geared toward coverage they will dust off the FB and run down your throat.
His teams have also been capable of playing multiple fronts on D going all the way back to the first title runs.