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[Archwizard]

And let's not forget that just because a job has barrier effects in the lore doesn't mean it will heal.

I mean, the Mhach raid has us undoing barriers made by Black Mages, who incidentally have their own shield ability.

Not to mention barrier healing itself is in a precarious position.

That being said my hopes are with a Chemist/Grenadier for the new healer role cause a lot of interesting mechanics could be used for it.

There's kind of a big reason I listed it as a Ranged DPS instead of a healer. (Aside from it expressly not being a Disciple of Magic.)
But when it comes to Chemist, you have to handle its trademark ability: the Mix command.

You got two big options.

One, is you have Mixing be an on-demand ability that functions as the core of their actions. Mix A+B+C to get a bomb, mix B+C+D to get a heal. It would make for the backbone of a solid rotation.
But if the job is primarily a healer, what if you need to stop a damage Mix to actually... y'know... heal?
Easy solution, either make it purely for damage or purely for support, so there's no crossover or potions blowing up in your face because the situation changed. But if you make it purely for support, you have to deal with a high APM task that other healers can handle with one spell (and they do their damnedest to avoid having to use GCD heals as often as possible).
And if you do it to attack...
Healers don't have rotations, for a reason. Notice how they only get a few essential skills for attacking, with an extra or two cooldowns (or pseudo-cooldowns, like WHM's Lilies)? This is because if they had a "rotation" of any complexity, even as simple as a 3-step combo, they would have to step out of that rotation in order to do their main job - healing. They get the basics so they can put it down and pick it back up at any time; their attacks are just meant to be filler between the moments of actual healing.

The other option, is you have Mix be a series of CDs you only use periodically, like the old NIN Mudras or the old AST Spread. Bear in mind that this is not only derivative and hard to make distinct from those two examples, but can mean several Mix combinations will go avoided or unused. The old AST spread got reworked because players were using all of their tools to try and game exactly one perfect combination. Even NIN already avoids Hyoton or Shuriken Toss, and that's in a damage capacity where its rotation could have been built to maximize use of all options - not a support role where the emphasis is on a few priority tools for select emergency functions. I can't name the last time I used Synastry as an AST, because healers are already drowning in higher priority tools.

Mix just doesn't really work for a healer - which is exactly the conclusion the devs came to when they tried to push CHM back in HW, and led to us getting AST with the remnants of their Mix system.

It would work for a DPS, however. Consider that first option again in the hands of a DPS (since the second is, again, just Mudras): Someone who has the time to consider what to mix, who can get mileage out of multiple concoctions in a row ("Here's a corrosive gel that will make the target vulnerable to my attacks, here's a blasting agent that will make my next hit into a napalm attack, here's a powerful incendiary that will activate the blasting agent..."), and can have a niche in groups through pre-selecting concoctions for powerful opening or post-transition bursts. (I mean if you only attack once every 3 GCDs, that third one is gonna hit like a train. Start mixing when the boss invuls, or when you see an add phase coming... you may as well be casting Death.)