Paul Brown founded the expansion Cinncinatti Bengals with a ragtag assembly of AFL refugees. In three years, he had thtem in the merged NFL Playoffs. Belichick considers him the GOAT among coaches, and worshiped him as a kid. The game never "passed him by". His great teams of the late 40s and early 50s merely got old; and he was rebuilding while still winning, when he got fired by jackass Modell, who also fired Belichick.
Don Shula was a victim of his own success. When his Superbowl clubs got old, he kept them still winning, but could never acquire quite enough talent to rebuild the team into a Superbowl team. But the Dolphins still have the highest winning percentage of any NFL team, and only had a handful of losing seasons as of last year. Two of which came while they were an expansion club, just gettiing started. IMHO, George Wilson doesn't get enough credit for assembling the Dolphins Superbowl squads that Shula inherited,and improved though.
So tell me what Cleveland or Miami have done since they left, other than Collier winning once, after inheriting the partially rebuilt Browns from Brown?
Belichick has been steadily adding talent to his rebuilt Defense. Sooner or later, possibly this season, it will achieve critical mass, and breakout back to a league leader in Defense. As for his Offense, he is putting the finishing touches on the final squad to be rebuilt.
Sooner or later BB will face the QB transition that Brown faced replacing Otto Graham; and Shula faced replacing Bob Griese. I think he is making sure the team surrounding the eventual successor/newcomer is prepared and complete. Meanwhile Brady still has a year or three to win another ring or two.