I guess I just can't see this, tbh. Other MMOs have a much more natural output of damage so that as long as a healer is moderately pushing their healing buttons and using cooldowns they shouldn't run into too much difficulty in casual content. I'm a casual healer in WoW (normal mode raids at best which are challenging but still completely puggable - think EX primals just in raid form) and never feel like "healing constantly" is this taxing process that requires a huge mental overhead from me. It just requires me to focus more on my party's health bars than the boss health bar, I guess you could say.
The biggest reason healing in this game likely won't change is because fight design would have to be completely re-tooled from the ground up to make it work. It's not as simple as "nerf healing potencies", because right now virtually EVERY fight in this game is about massive burst damage followed with lull periods (usually incoming one-shot mechanics where players are not expected to take damage unless they fail the mechanic) to allow healers to get value out of the regen/oGCD aspects of their kit. Imagine something like Almagest at the ilevel most of us were when we started O4S, but imagine healing power arbitrarily cut in half - a single Almagest round with that dot would probably force layering just about every regen you have along with AOE heal spam between, and your mana would be tanked before you know it. Now if you're saying, "just halve mana costs too, np", well how does that affect periods where there's just single-target damage going out? You're suddenly keeping one person up with a lot less effort/opportunity cost, especially between two healers babysitting them. Healers would probably still be DPSing there, so you'd still keep that same DPS focus for single-target/tank healing but make AOE burst damage a lot harder to deal with for no real reason.
In other MMOs damage is a steady, constant ongoing stream with very few spikes/danger areas. Healing in, say, World of Warcraft is more about stemming a slow bleed with your resources than about efficiently powering through massive near-teamwipe damage with as few casts as possible (and DPSing in the interim). Unless that aspect of XIV healing changes, I don't think just "nerfing healers" will produce much of an effect. Even tank cooldowns are oriented around that burst-type damage - there's virtually no "low CD, medium impact" tank cooldowns that tanks are expected to rotate constantly to mitigate steady sustain damage, it's all about waiting for the boss to do his super move and rip something like Vengeance or Sentinel, then wait another minute or so before ripping something else for the next tank buster (or tag in your OT with Shirk and go full DPS mode yourself to get maximum value out of mitigation CD timers). The gauge abilities like Shelltron come close, but I find they generate too slow and bar Inner Beast don't have enough of an impact to encourage rotating them (and even then I bet more WARs use other CDs to mitigate and save Beast Gauge for Fell Cleave).
Whole fights would have to be changed from the ground up to make room for any sort of changes to healing design. With XIV's level sync enforced for pretty much every roulette you'd have to check every trial, every dungeon, every 24-man raid to make sure that nerfed healers can keep up with damage output without difficulty, and you'd have to design all future content going forward (including possibly some already partway through development) around this idea of more "heal-oriented" healers.
Would I love it? Sure. Do I see it happening ever, given how little SE seems to want to a.) disrupt the status quo, b.) invest significant resources into this game (see: housing, server limitations, etc), and c.) enforce a playstyle change that frankly would be pretty disliked by a not-insignificant portion of the healer playerbase (if healer subforums and Reddit are anything to go by)? Nope.