There is some definite truth to this, but cap issues aside, he definitely gives you your best shot until he leaves the game. I don't think Aaron Rodgers is really the problem for the Packers right now, its how do they keep Aaron Rodgers and keep a competitive team. If the Packers had $40 M in cap space, I don't think this discussion takes place. Rodgers stays in GB, they sign Davante to a huge deal, hire a new special teams coach and fill a few holes with FA signings, trades or draft picks.
Basically, what I am saying is that Aaron Rodgers isn't the one that is necessarily triggering the "its time to move on from him and rebuild." However, if he doesn't want to stay in GB, than yes, he is triggering it.