There are lots of preferences here, I'll try summarize my current view a bit better:
Magical healing should exist. Magical healing should not act to simply extend combat. Therefore magical healing in combat should consume a resource that could be used to do something else.
Clerics should not have to be the ones consuming those resources. Besides, not all deities really go in for healing. The healing deity does though, of course, so his or her Clerics are probably happy to consume their own resources to heal. These need to be limited in some sense, however, so that this type of Cleric doesn't become essential.
I propose that there exist rituals to grant healing outside of combat. The party makes a decision to turn a communal resource, gold, into healing. The creation of healing potions should also be a ritual, at slightly greater cost. These rituals should be available by use of a Heal (Wisdom) check. Hit dice are sort of achieving this, and I think the ritual could integrate with spending HD.
In combat, a character can use healing potions (a party resource), and there could be a second-wind action to spend a HD (his or her own resource). Clerics of the lifegiver will then be the only clerics able to heal, preferably via channel divinity. The divine speciality should give access to a specific god's channel divinity powers, hence anyone could in theory be the healer.