Part of the issue is that healers are very inconsistent and not user friendly. Only some of them are selected with the military gather command (Griots, Abuns, and Warrior Priests aren’t), and only some of them actually function as they should when you command them using attack move (Griots use their stun, but some just start punching instead of healing).
Some of the new healers like Abuns and Griots actually are really good so what they need to do is just buff the rest to make them usable. Surgeons should be able to heal in battle at least as well as Abuns can. The rest of the healers could be given area of effect healing to that they can more effectively heal. Another option could be to let normal healers could continue healing a unit that enters battle, as long as they started healing it while it is at rest (at least for a short duration).