I don't understand how people can't see anything beyond we already got, really, there's different Healers in many games MMO or not to take inspirations, FFXIV don't have all possibilites already and nothing new can be done.

Said that, we have 4 Tank now and they are similar in some points ( PLD and GNB, WAR and DRK ), the same can be done with healers.

Ex:

WHM: Massive Healing + Regen.
SCH: Massive Shields + Mitigation.
-----------------
AST: Regen + Buffs.
New Healer: Mitigation + Buffs.

Nocturnal Stance can be removed, a melee gameplay style for the new healer would be awesome as well ( Melee for Damage skills, Heals/Buffs remains as Ranged skills for obvious reasons, like PLD, they are a Melee job but Clemency is a Ranged skill ). They can have some skills like AST old card system, mixing potions to have some special effect like buffs ( assuming that the new healer is like Alchemist from FF series, a Healer job based on Potions manipulation ).