All healers have access to Lucid Dreaming, so we can forget about that for now. On top of that WHM/SCH have a 10% MP recovery every 60 seconds, with both having a way to decrease the recast time (Assize/Aetherflow), and AST can extend the duration of LD to make up for that. Each job has one more MP regen ability in the form of Thin Air, The Ewer and Energy Drain. All but WHMs are situational, and WHMs one also happens to be the strongest if you utilise it correctly, with SCHs being the weakest.
As I'm highlighting a potential SCH weakness, I'm going to compare it to N.AST.
Technically our AoE heal is also a lot more expensive if we're using Emergency Tactics as you have to compare Succor MP costs to Helios, which is 1326/1061.
- Adloquium - 1061 / Aspected Benefic - 707
Arguably the most used tool for the shielders, you can see that Adlo has a much higher cost. Which considering it's weaker and has a cast time makes no sense.