In the Princess Bride, they bring Wesley back to life just by visiting an old cook.
It's more common in religious mythology. The Bible is full of healers of the sick, destroyers of the plagues, etc. In many shamanistic traditions, the shaman is responsible for keeping away sickness and combating the spirit that causes it.
Indeed, the belief that infections, insanities, ailments, and, indeed, death, come from hostile spirits and not from physical and biological problems is pretty pervasive in human belief, so the "religious figure as healer" has a strong tradition. Lump that together with the "advanced western medicine," and some times, even in the modern day, missionaries become doctors and care for the wounded. And doctors = witch doctors as far as many tribal societies are concerned.
For my milage, if we're going to let wizards throw fire from their fingertips, we can let clerics make you feel better with a touch.
It also works well with a description of damage that doesn't ALWAYS include a wound. If an hp loss is getting a ligament torn, getting the wind knocked out of you, tripping a little bit, and generally just wearing down your endurance, it's not that the clerics are repairing dagger cuts as much as they are repairing your energy and vivacity.
Magical healing of one form or another is rediculously common in religious myths.