Scoring, especially scoring in half court sets, is what gets you through rounds in the playoffs.
Parker is a PG, who's an elite scorer; scorers are featured prominently in the playoffs because of the lack of transition and the usually strong defense of the teams that remain. His scoring ability in the half court is at a point where he has more than one option in the P&R alone and he uses each option to full effect.
Chris Paul is more of a distributor than Parker, but in the playoffs, he becomes as aggressive of a scorer as Parker is and as a result an even better scorer. Why doesn't he advance in the playoffs then? Coaching and personnel (how do you think teams win double-triple teaming Paul?... the gameplans have been to get and keep the ball out of his hands). CP3 is still the best PG in the league...
Rondo can become that, but he has to continue to improve. When he starts to average 18-22 PPG, he'll be that. Until then, he's not as built for the playoffs as the other 2.