From a raiding perspective, I'd say that avoidable damage doesn't have a huge impact on healing, because many mechanics will simply one-shot you if you fail them. Probably more significant is the use of damage mitigation. But the most significant impact on healing might be the level of your party's gear. Higher level gear has several relevant effects. It has higher defensive stats, which means less damage taken. It enables you to kill bosses faster, thereby skipping mechanics with high unavoidable damage. And it increases the amount healing done per healing action. So in general, the better your party's gear, the fewer healing actions you need to use.

Consequently, the amount of resources that healers need to devote to healing diminishes over the the course of a raid tier, as their party's gear (and performance) improves. This presents a problem for developers. If they tune jobs and encounters so that healing remains demanding, and therefore engaging, even when players are fully geared, then it may be too demanding for players with only entry-level gear (e.g. everyone at the start of raid tier).

Some possible solutions:
  1. Other MMOs solve this problem by having larger raid parties and less rigid party composition requirements. Whereas a less well geared (or less competent) party may choose to take 4 healers, a better geared party may take only 3 or 2. But this may be too drastic a change for FFXIV.
  2. Another solution is to make healers' non-healing functions more engaging. But SE might worry (perhaps with justification) that this would distract some healers from their primary function of healing. And anyway, some healers want to be healing, not doing other things.
  3. FFXIV already implements a solution to this problem in ultimates. These have a fixed item level sync, so you can't "outgear" them. Perhaps the same model could be adopted for other kinds of content, like savage raids. But then the gear awarded for clearing this content would have less benefit. Having said that, people still do ultimates, even though the only rewards are prestige and a sense of personal achievement.