Doing those things short term when teams don't know what to expect is different from doing them for the long term when teams learn what you will do with that QB and how to attack you.
Would it make any difference if I said "Bridgewater played as a slightly above average game manager" when he had to starts in relief of Brees? Because the offense at it's best is a high scoring big play offense, not a dink and dunk traditional West Coast system run by a "game manager."
The point is that every QB other than Brees resulted in the offense being more dink and dunk than a big play offense. Payton was a good enough coach to win a lot of those games with that style, but it's not what the offense was meant to be and couldn't carry the team where they wanted to go.
And, I think the difference between the Payton system and the "Shanahan system" is that the Payton system puts it all on the QB to control everything and make all the plays where as the "Shanahan system" takes pressure off of the QB by giving him easier throws, receivers with mismatches, easier reads that don't require scanning the entire field, and by giving him information about the coverage with motion. It means that in a age where QBs change teams more than ever and so few college QBs come in prepared to run something as complex as Payton's system, can come in and immediately be competent in the system.