As far as FF lore, the Sage was often the ultimate DPS upgrade for your mage class. Both good healing and good damage magic, but the focus was damage. And it was healing magic, rather than shields.
On the other hand, the Green Mage is all about barriers and buffs and (lesser) heals. I have always loved how FF has Black, White, Red & Blue Mages. It is natural that I want to see Green added to the mix!
There are 3 healers currently and 3 types of heals: direct heals, shields & regen. But Sage would add a 4th healer.
How about AST, WHM & SAG(?) each have 1 specialty that they do consistently and do well?
Then have Scholar be something extraordinary. High risk, high skill, high reward. SCH could do all 3 things and do them better than the specialists! But they could only do them on a limited basis and there would be significant cooldowns. It would absolutely be about tactical decisions made on-the-fly. No way for SCH to spam an ability if things go tits up. Either Scholars will be godly or instant-death, depending on who is using them. Also, the SCH pet would now be directly controllable again and Eos and Selene would be quite different in abilities.
I have dreams but I think this one would be tons of fun!