Sage is NOT: A DPS-oriented barrier healer.

Sage IS: An OGCD healing oriented regen healer.

Sage's most used healing resources are Kerachole, Ixochole, and Physis II. What do they have in common? All three have nothing to do with DPSing other than enabling you to spam Dosis III more and nothing to do with barriers period. Meanwhile, Kardia, the thing that is supposed to be the heart of Sage's healing identity has no way to interact with it, no way to address different healing requirements, and almost no reasons to ever actually pass it around to other party members. There are certainly situations in which you can swap it to other party members, but the effect is too slow and too weak to have any meaningful applications in tighter healing requirements in which healing resource management actually can be an important choice to make. So the only times where passing Kardia around to heal actually can be used is situations in which there is no pressure on your other healing resources anyway. Sure you can use Kardia, but you could also use literally 20 other buttons for the same thing. In fact, using your Addersgall may very well be a better use of resources than Kardia anyway since you're more often than not drowning in Addersgall that you'd like to spend on actual healing to restore your MP rather than either wasting the healing when no one needs it for the MP or just foregoing the MP altogether.

And that doesn't even go into how little Sage relies on barrier application as a "barrier healer." Haima and Panhaima? Cool, but also niche and on long cooldowns. Holos? The barrier was added as an afterthought and is also a long cooldown resource. Eukrasian Diagnosis/Prognosis? You mean the two objectively worst healing actions you can possibly use other than vanilla Diagnosis/Prognosis or Pepsis: the skill that's utterly garbage specifically because it relies on having the barriers from the almost equally garbage GCD barrier heals that a good Sage never touches?