Chemist = Healing mudras is something I have wanted since Ninja was a thing, I think it is a great idea and works for XIV. The weak arguments I have heard against it are A) Alchemist already exists - which is countered by calling the job Salve Maker, and B) Mix just makes it a harder to play healer with the same payoff, which is why I think that Mix should be purely for buffs/debuffs/damage, like AST. The megalixers/X potions etc. should simply be cooldown heals like Lustrate and Benediction.

To further refine your idea, I would name their raise "Revive" instead (as it is in FFV) and make their LB3 "Final Phoenix" (named after the mix command from FFX).

I think Chemist is a great idea because of the lore implications, the job could be tied to the NPCs of the alchemist guild, and the weapon itself could have an interesting design. I always imagined it as a kind of "aetherial grenade launcher" that the chemist uses to mix the salves and shoot them at allies and enemies.

Edit: Oh, and the Job gauge holding the mix commands works perfectly (imagine a cauldron filling up)