Don't forget mystics also get a wolf pet that not only adds to their dps but heals as well. And while yes it can die, it also keeps fighting when the owner is healing, something the other melee priests can't do.
Off topic but in my limited experience the shaman classes are hands down the best priest on a raid. From what i've seen personally despite there being almost 2x's more furies than any other priest class they are always at the bottom of the healing charts with mystics at the top, and clerics in the middle. It's the nature of wards vs regens, a mystic casting a ward on MT is guaranteed to get the full healing from the ward, whereas most regen tics do nothing since mt is at full health.