WHM has two regen abilities, single target and AoE which also stack with another WHM btw. Stoneskin to mitigate damage, Another AoE heal, Cure and Cure II which is a heavy duty heal plus they have benediction as an emergency heal all on a target. If something bad happens a WHM is just better placed to fix everything. Base AoE heals might come close but if a WHM uses Divine Seal and Medica II the SCH can't even approach that level of regen on the whole party.

SCH has the advantage of making it easier to keep up mana but a good healer won't run out of mana easily anyway. They have better damage mitigation skills but their healing ability doesn't touch WHM. The Fairy is all fine and good unless you consider the fact that it's not very reliable. The Fairy effectiveness depends on it being in a fight where it won't get hit by everything and get stacked with debuffs all the time.