It's interesting to contemplate, but according to Coriel priests are actually the hybrids of the healing genre. The other healing classes focus on one type of healing. Druids have their great heal over time abilities, shamans have chain heal, pallies have great single-target heals. Now the priest is able to do all these things, but none to the capacity of their fellow healing classes. Therefore Coriel says, they are the jack-of-all-heals, and the master of none. Further down in the comments to this post a commenter also brought up the fact that shadow priests are also hybrids, being a dps/healing class.
Is this why the priests of WoW have been having a tough time competing in the more challenging healing situations? What could Blizzard do to establish priests as the kings of healing once more, or is their very nature holding them back?