Besides the poor aw abilites, the other reason why i didn't recommend healers as the top 3 awakening candidates is simple .
Awakening orb maps/daily mission X maps - having high DPS makes clearing maps easier. (UP is tight so high dps compensates for lack of min-cost units) Their difficulty lies in clearing mobs fast enough while dealing with low UP (hint archers are gud)
You'll only really need AW healers as you approach the awakened fairy maps, where they allow only AW units.