It's a different discussion because FF14 already has established healing classes. To uproot them and change their mechanics in order to fit a new healing paradigm would be doing their players a disservice. Adding new Jobs that have a more specialised usage would leads to the situation you described where players are forced to use it for specific encounters only, unless you have another Job that compliments it well. So already we'd need at least 2 new healing Jobs that would only function properly when played together, but would out perform any other combination of healers.
Which then leads to the existing healers needing buffs to compete, which in turn leads to the new healers being buffed and so on.
Even with in the constrains of the current game, the idea would fundamentally work without serious changes made to content.
Specialising is more about numbers and abilities rather than design which is where the issues would lie - You'd need to redesign your Jobs around it more than your content.
Going forwards, having new healers that are just another carbon copy of the WHM is going to get stale soon, so sooner or later having one that's more specialised towards a certain role is going to happen if they want to break the mould. It's not just healers, tanks are in the same boat too. Adding yet another tank that plays the same is going to get repetative.
Is that something that FF14 should strive for? Well, that's the question isn't it. Do you want more of the same with some gimicks, like the AST, or do you want new Jobs that feel, well... New. I'm sure you can find people who come down on both sides of the argument. It's a far more nuanced issue than just the current constraints.