Having not played in a while, I could be off.

It used to be that the Druid was the most mobile of healers.
A lot of their heals were instant cast heal-over-time.

That said, I personally found a Resto Shaman to be great in instances.
The Earthshield was a very strong mechanic, for the tank.
A benefit of going Shaman was the dual-spec option.

Earlier in an expansion, my 5-box PvE team consisted of:
Tank: Prot Paladin.
DPS 1: Demonology/Destruction Warlock
DPS 2/3: Elemental Shaman
Heal/DPS 4: Resto/Elemental Shaman

Earlier into an expansion, or switching to heroics after finishing the normal stuff...
It would be Prot Paladin, Resto Shaman, and 3x DPS on their click sequences.
The Shaman would have a mapped key to enter/leave the DPS Action Target Group.
So as a healer, my spam wouldn't do much aside from rebuff Water Shield and Earth Shield periodically.
Most of the controls were manual.
But I could respec the Shaman to Elemental (once that was introduced), and add them to the DPS ATG.

Later in the expansion, 3x DPS had enough healing with the Light/Fast heal.
And more DPS killed things faster.

The Earth Shield was essentially mobile healing, in that the tank was healed each time it was hit.
And dropping totems is on a single GCD, for all of them.
The healing stream totem did a fair bit of healing, with Resto spec.
The Paladin did have a few invulnerability abilities, for an emergency situation.
And the Shaman could self rez, for recovery if need be.