The reality of how this game is designed on a fundamental level, though, is that DPS contribution is the most important metric you bring to the table regardless of your role. This includes healers. This cannot be changed with massively overhauling the entire game's combat design, which includes reworking every single dungeon and trial. The reason for this is because damage is way too infrequent to push you to needing a healing-focused playstyle. This is true of every RPG really, even the old Final Fantasies. If you've ever been under leveled for a tougher boss in an older Final Fantasy, and found yourself using all your turns to heal with magic or potions, you'll eventually get overwhelmed and fail. RPGs are defined by your need to push out as much damage as you can with every turn. Choosing to heal takes this into consideration. If you don't have someone heal, and a party member dies, that's a huge hit to your damage output.
Having said that, it is entirely possible to design a healer who contributes their DPS passively by applying buffs rather than by mashing an attack spell. It's not a fleshed out concept, but on another topic discussing the upcoming AST rework, one idea that came to mind was if you split draw into Astral and Umbral Draw, giving you offensive buffs and defensive buffs, and making both drawing and playing your cards GCD actions that additionally cause a star to orbit around you to a maximum of 6. When you cast an offensive spell, one star delivers an additional attack of the same potency as your DPS nuke (currently 250 on Fall Malefic). You can then use Astrodyne as an OGCD action to pass your stars over to someone else, and when they use spells or weaponskills, your stars will attack with them with the potency stemming from you.
This would give us a healer that has a more passive support playstyle while still contributing DPS.