If you are wanting healers to have something to do, but it not be damage necessarily:
Reduce the potency of AoE Heals and have them cost much more MP and/or have them nott effect all players, such as the 4 lowest hp players.
Remove most oGCD Heals, or put them on very long CDs.

This is to promote using single target heals to keep up the heals rather than 2-3 AoEs to bring players from 0 to 100% hp. The simple DPS rotation is still simple as you will be spending most of your time healing each player and you be spending much less gcds for your dot and single-target attack.




If you are wanting healers to have a more complex DPS rotation only:
Add a random proc to the single non-dot spell to use a different spell. For instance:
"Glare 1 and proc the ability "Burning Light". It deals more damage than Glare, has a short DoT and/or refreshes/extends the duration of Dia."
Dealing damage reduces the cooldown of a heavier hitting spell that has a cooldown.
Your DoT has a chance when it deals damage to let you apply a different, but shorter and stronger DoT.
Casting <Insert Offensive Spell Here> ramps up damage from kinda low dps, to higher DPS the more you cast it.

You really can do anything with these the DPS part of a healer and have it have even just a small more degree of depth, or even have it loop back into healing a bit by increasing the potency of a healing spell in some way when you deal damage.


Overlapping Ideas:
A CD that makes your shields deal damage to enemies when they are completely consumed.
Your spamming DPS Spell reduces the damage of the target by a flat damage amount and can stack to a maximum set amount.
Kardia being set (maybe as a CD) to heal everyone or heal whoever has the lowest HP in the party, for set a time.
A abilitiy that changes some WHM spells to deal damage instead. Some examples are like Asylum becoming a huge AoE DoT on the ground or Cure 3 being a large nuke. This effect would probably would have a CD.
A trait that, when you Heal you progressively heal less and less each cast, but increase your damage. This would also reduce the MP cost, and increase the recast time for healing spells.

I know these ideas are not perfect, and they might not work the way I'd hope in reality. However, I dont think it makes sense either that we are several expansions into FFXIV and there is not really any innovative ideas in the case of healing. I don't mind something simple, but every healer is you either heal, or you deal damage and there isnt really much overlap in those ideas, aside from a few that are just tacked on to a class., such as Kardia, Earthly Star and Macrocosmos.