I don't think a job should be pinned down as some kind of pure full support or full healer because support and healing are two different things. consider the utility of stoneskin vs the use of cure. You focus on prevention before the cure. That being said, you could actually separate those responsibilities between different party members. This can allow for more diverse party set-ups and evenly distribute the responsibility of party members.

---HEALERS---

-Gladiator-
I think paladin should be refocused for stronger healing along with its tanking. I feel like thats the
paradigm it best fills.

-Arcanist-
Scholar would be pretty good. It could shift between DPS and healing.

-Thaumaturge-
In my job speculations I considered necromancer with sacrifice ability and raise stemming from conjurer. This is a DPS/PET/HEALER hybrid, allowing you to sacrifice pet a cheap pet for a cure. In addition, a necromancer should be able to perpetually come back to life in the way an undead does.

-Conjurer-
White mage is your typical healing here.

-Pugilist-
The Dancer job would work effectivly with something like drain samba making a reappearance. This would help dancer to be mainly an enfeeblist but give it a healing element.

---Support---

-Mystic- (a support orientated class I made up) It would become time mage or arithmetician. This is a class that would bolster great utility but doesn't necessarily have healing.

-Conjurer-
Conjurer is already our prime candidate, but suppose a job such as Geomancer came to it. Geomancer would refocus on DPS and support, rather than support and healing.

-Archer-
Again bards great utility makes it a support role.


These are just a few examples but mainly the point I'm trying to make is that we need to stop forcing support and healing to be under the same roof. They are two different actions that need to be diversified into more jobs.