I wish they had implemented it this way too and was disappointed that it wasn't so. I would prefer it if the limit breaks were by class with different additional effects that relate to the class' lore (and if there were a separate limit break bar for each player) instead of the copy-paste same-potency, same-effect, different-animation silliness we have now.
For example, the SCH's niche is that it's the damage mitigation/DPSing healer. SCH could receive an AOE heal of X potency that creates a unbreakable barrier that reduces damage taken by x% and restores HP equal to the effect of the barrier each time the target is damaged, lasting a duration of Xs. This plays into both of its characterizations, making a barrier that also heals which frees it for more DPS time.
WHM is the raw potency healer. WHM could receive an AOE regen that increases each target's reception to healing by X% on each tick for a duration of Xs, the increased reception to healing lasting a duration of Xs after the final tick. This affords it for even more raw healing for that next Cure II.
To me, there's just too many possibilities for the uniqueness of LBs for them to not have been implemented by class and with less homogeneity.