White Mage is my main, so I am here to defend it. ^_^

WHM is the pure raw healer of the three.
The other two can not come close to the raw healing power and MP Recovery that whm brings.
A great WHM within a seasoned group can solo-heal a run and put the other healers into DPS mode.
In tight-healing, the WHM can save the MP of the other healer by having the group stack together and Cure III (or Assize).

Sure, you can talk to me about those special skills scholar and ast have for recovery, but those are just "Special" and not "Standard" and so here is where we hit the great divide.

Developers have stated that all content is designed so all healers can get through it. This means they will not make a boss that requires super massive WHM level AoE healing to the point AST/SCH wont be able to keep up without spending too much MP. However, they won't make a boss that has SUCH an extremely powerful attack that without shields, the entire party will be wiped on a single hit (outside of failed mechanics).

This means the shields won't ever be greater than whm's raw healing.
Still, all three healers are "Doing it wrong"

The purpose of shields are to TAKE THE HIT in that 30 second time frame and finish your combos, not AVOID taking the hit.
So when the shield is applied, but the players do not take the hit, its just wasted MP. However, white mages do not use cure iii enough. You know, you can save the other healer MP and also increase group DPS by simply saying "Oh just stack at that one attack, take the hit deliberately and ill Cure III" instead of always doing that at mechanics-only.