How would they even make another healer job though?

[Eloah]

GNB does through its normal combo, though it's nothing major.

WAR and DRK do that as well, but with their combo ender, not the middle section.

From those two things, you'd follow the basic healer kit shared across other healers:

Basic heal
Large heal
AoE heal
Instant heal
Specialty heal
AoE specialty heal
Raising spell
"Increased healing" cooldown.

While this seems to be a good generalization, it's a bit inaccurate. SCH doesn't have a Large heal, nor does it have an AoE heal, but it does have the faerie to compensate for the lack of those skills. One could argue overlap in certain areas, but seeing as both AST and WHM have individual skills that fall into the specific categories you listed, the skills SCHs lack cannot be ignored. This is what makes SCH the outlier, which isnt bad, but it's why SCH is a bit more difficult to balance compared to the other two.