Honestly, Sage requires you to be a bit of a paranoid Healer, and prepare for damage rather than react to it. It is very much like 2.0 Scholar where you prepare and null damage before it happens rather than following the White Mage/Diurnal Mindset.

Funny enough, your Ex Diag is where you get your punch of healing. The job very much does evolve its priorities as it gets higher on in level, requiring you to shift your focus from Dro to Kerachole and Physis as your go to combo. Terachole is your bread and butter, and you should basically have those on cooldown at all times in dungeons.

Sage doesn't really struggle with getting hp up fast, but the methodology is very much different than the other healers. Sage definitely does require a more practiced hand from a veteran healer to use effectively out of the gate, as knowledge of previous mechanics and healer Spidey Sense help as well.