Reading the OP, they've sensed something important missing. Every compelling MMO class has a Crowning Moment of Awesome, but healers largely don't in XIV. DPS can, at times, but healers? Not so much. Let me tell you a story about how a healing class stumbled into being great in another MMO.

First, imagine a kit whose cooldowns all synergize with each other - and it has roughly five of them. These include a ground-bubble that boosts healing within it, a fat ground-targeted AoE heal that copies itself a few seconds after it's placed, an ability that starts copying a % of healing done when pressed and then releases all the stored healing after 15 seconds (or when pressed again), and then two bog-standard large percentage increases in healing (akin to WHM's two % healing boosts). Every single one of these abilities had a different cooldown, from 30 seconds and 45 seconds to two and three minutes.

As with tanking, most of the time you'd only want to use one or two at once in order to survive - anything else would be wasteful overhealing, after all. That's not unlike current XIV healing. But every so often, a fight would have a section or two designed to test the healing team. And then, because you've planned and saved your cooldowns, setting them up in advance to be properly layered... you blast out an order of magnitude more healing than your baseline standard. Quite literally, up to an order of magnitude when executed correctly.

Those moment feel incredible, but there is nothing like it in XIV healing because the kits are almost entirely linear rather than multiplicative. There isn't anything like jamming Resto Shaman cooldowns into Aggramar's DoT phase because only WHM could get even close to meeting such a challenge. That leaves the experience feeling... flat. Without peaks. The closest I've gotten is the satisfaction of setting up layered shields as SCH at just the right time during early progression.