I would offer that there are two issues working towards why Patriots players are not serious Hall of Fame candidates. On offense the ball gets spread around a lot. We see the stat every game: Brady has thrown to nine different receivers. So it can be hard to get big numbers unless the player really clicks a la Gronk.
I would say the second reason is not just Belichick getting rid of players but how many players get signed away from the Patriots. At this point, how many really good players are left on the Patriots that are free agents? Flowers may have been the best left and he got signed away. But how many teams are clamoring for Hogan? Solder got a huge contract from the Giants so the Patriots had to rely on Trent Brown and he was pretty serviceable. Patriots win Super Bowl and Brown becomes the highest paid left tackle in football. Second year in a row Pats have to find a left tackle. And often times, Patriots free agents sign big contracts but don't put up huge numbers justifying those contract pay outs so the easy labels is those players were just a part in the Patriots system. Well, maybe in the first place the Patriots paid those players their true worth and did't get suckered into paying a good player superstar money.
So that's my theory on the subject.