I can sympathize with fulminating on this, I think having core relations to job fantasy of its roots is really important, and the state of healers is abyssmally bad right now.

I have to stretch with my thoughts on SGE as "a healer that can heal while DPSing" with the idea of classic FF being "can cast high level White/Black/Summon magic with limited MP" identity. They certainly aren't using any White/Black/Summon magic in FF14, but given they wanted to focus on healer identity with SGE as a barrier healer specifically, they tried to make it fit by saying "they can heal with Kardia while doing damage" which kinda' fits if you really push it, but I completely sympathize with why she isn't satisfied with that.

As for the Greek names being exclusive to Ascians/ancients, I never really considered that before but also is a good point.