Why do we need more game play than we already have? It's more than what DPS get.
We need to heal someone? We have more than one single target heal to use. We need to heal multiple party members at the same time? We have more than one AoE heal to use.
We need to react to mechanics just as DPS do (or don't since we can always rez them if they try to greed and fail).
We need to watch the boss HP and cast bar to time our use of our more powerful cooldown when needed.
We need to watch party member HP, buffs and debuffs to know when healing is needed and how much, to know if Esuna is needed.
The exceptional healers are even watching where party members are standing so they can Rescue them if needed and available.
DPS game play already stops short of where healer game play does. Why aren't we hearing complaints about a lack of DPS game play?
The big difference between the two is that the DPS experience is generally consistent. They rarely need to alter their focus while the healer does frequently if not constantly. The healer experience varies depending on other in the party. Skilled players mean only needing to worry about unavoidable damage. One or more lesser skill players means needing to keep more constant watch on the party (is the less skilled player standing in mechanics, are they stacking on others when they should be standing apart so more party members need healing, etc.).
That is why SE has to use caution in designing healer responsibility in normal content. Not only does the healer need to be able to adjust to what the party is doing, different healers have different reaction times based on their own skill and familiarity with the content. That is expected in normal content that is meant for everyone while in more difficult content, players are already expected to understand how to play their job and react to mechanics correctly (outside of a short learning period when they first start working on the content progression). That allows SE to increase expected healer responsibilities in that content, theoretically creating a better game play experience for good healers.