Personally I agree that this is probably one of the reasons that some healers end up not nuking at all with Cleric Stance.
As you go through class quests, oftentimes as a healer there are NPCs with you that'll attack the enemies for you, so it can be easy to forget that you're expected to be both dealing damage and healing them. With so many levelling options now (especially PotD) I think it's easier than it has been before to level without having to play solo. I think if they made Cleric Stance more important (not required of course, that would be a little unfair) for simpler things like class quests it would be easier for some players to understand the dual-nature role of healing. Even if it was just something like an NPC saying "hey that Cleric Stance ability would really be useful while we go fight X enemy / Purify the taint / w/e", or "hey have you heard of that Conjurer ability Cleric Stance? You should find a way to get it so you can help us fight". Even if it's just a passing comment.
I understand that there's already things in the game that make it clear a healer should be doing both. But there's no way to guarantee that new healers are going to take part in the Hall of the Novice / keep up with the forums / etc. And of course, some players who aren't in an FC/LS with more experienced players or simply play alone may genuinely not realize how much using Cleric Stance and DPS can contribute.
Making Cleric Stance more important and maybe having a class quest or two that require Cleric Stance would help new players gradually build up their skill with stance-dancing instead of getting to level 60 and realizing "oh wait I'm not supposed to heal all the time?". Not to mention that it's pretty much guaranteed that Cleric Stance will become a shared role ability, so new healers in Stormblood will all be able to use it naturally.