Paul Pierce, up until this last season, had one of the most durable bodies in the league. In contrast, his western coast peer Ginobili, went south starting 2008. Thus, in terms of clutch performance & long lasting plays, Manu was not the man he was, before that year. With that in mind, Pops did not have a one-two punch, which he could rely on, playoff series after playoff series, as in PP-KG. He had to improvise and in this league, stars win playoffs.
Next, if Parker had started with the C's, he'd be warming the pine for much of his early years, playing a role not to distinct from a Tony Delk or a JR Bremer, as oppose to Eddie House or Tony Allen. Hence, he'd probably be traded, as Doc wouldn't see his natural brilliance in bolting *no look* passes to the big three. In contrast, Pops pushed TP for years, and molded him into the JoJo White that he is today.