Variability of outcomes is higher in a short playoff series, in other words more luck is involved in the outcome, and the effect of player quality on the outcome is reduced. Over 162 games the effect of luck is minimized, and whether a team makes the playoffs depends primarily on the quality of their players (and injuries of course).
RP don't become more valuable in a playoff series. BUT, the results can lead to an erroneous perception (i.e., yours) of the impact of RP. Fact is it is just statistical noise.