I've been thinking a bit about healing in 5e, and I've noticed that there's a tendency (especially, it seems, among 4e fans) to treat it like a side of vegetables you're served with dinner. Nobody likes it, the theme goes, but it's part of a balanced meal, so they try to mix our peas in with our mashed potatoes (heals as pseudo-minor-actions so you can attack in the same round). JUST healing would be too boring!
Well, for prettymuch the whole run of D&D, there's been this perception that the cleric is a boring band-aid class. Critically important, but dull. The class the last person to roll up a character gets stuck with. The newb or 'girlfriend' class (yeah, that's sexist, so was the game 30 years ago) so the un-involved player could make a contribution without having to pay much attention nor take any fun away from the serious players.
3.0 first tried to change that. It did it by making Cure spells 'spontaneous,' that way the Cleric didn't have to memorize whole slates of cures, he could have other things on tap in case they came up. It also gave the Cleric more 'buffs,' including self-buffs, though it made physical-stat-boosting and other buffs you'd cast on the party melee types much more efficient.
3.5 tweaked things only ever so slightly. Made some very efficient buffs a little shorter duration, added mental (thus save-DC setting) stat buffs available and equally efficient.
CoDzilla was entirely possible in 3.0, but it turned virtually inevitable in 3.5 - all just from trying to make the dull Cleric class a little more desireable.
4e also tried to make the healer role a little more enticing. To start, they changed the name to Leader. It didn't fool anyone - the one thing /every/ 'leader' class had in common was a 2/encounter heal! - but I guess it didn't hurt. It also shifted the resource burden of healing from the leader to the individual character. Everyone had their own ample supply of healing surges, so the Cleric no longer had to prep whole slates of Cure spells or end up spontaneously casting most of his spells as Cures.
The Cleric could still be a very effective healer - with the introduction of the 'pacifist' build even a dedicated healer with a wide range of healing options, but it could be more than that, if desired. Other leader classes took healing as more of a side-line and concentrated on buffing or affecting the action economy.
But, all those people who like to play healers might enjoy seeing a broader variety of heals in the game. To my mind, it's those more varied heals that should be domain spells for the Lifebringer domain. Cure X Wounds should be relegated to Channel Divinity so that all clerics can toss it in on top of a melee attack or orison.
Well, in 4e, your Cleric, specifically, could choose to take utilities like Cure Light Wounds, and powers that allowed surges or restored hit points or granted temp hps, or to largely avoid all such, limitting it's healing to the obligatory Healing Word (enough for the party to get by, certainly).
Clerics, in particular, had a lot of different ways to handle the healing aspect of their role. They could use Healing Word to trigger a surge and give additional bonus healing. They could optimize to increase that bonus. They could choose other powers to 'trigger' surges for their allies. They could use 'pacifist' powers that don't directly damage enemies but grant allies non-surge healing. They could give allies temporary hps as pro-active healing. They could grant regeneration. They could give up their own hps or surges to heal allies. They could set up healing that triggered when allies inflicted damage. They could heal off-turn with immediate actions.
Other leaders weren't without variety in how they handled healing, either. Artificers could manage surge use among their allies as well as simply trigger surges. Warlords could heal with their mere presence. Bards could maximize between-combat healing.
So, there's already a lot for 5e to draw upon when it comes to jazzing up the 'healer' role.