Saying that Kardia heals when the Sage is ''doing damage'' is like saying that the fairy heals whenever the scholar is ''doing damage''. Both are true. But it's not a selling point. It's not an inherent advantage over the fairy. It's just a requirement that the fairy doesn't have. It means that you're not healing through Kardia whenever you're not ''doing damage'' And ''doing damage'' as Sage isn't different from scholar anyway. You cast phlegma instead of energy drain, cast dosis instead of broil, and you cast eukrasian dosis instead of biolysis. They are identical in use, and nearly identical in potency.
Again, there is no inherent advantage or unique synergy here.