I want to see the actual healing rotations become more involving in the sense that performing basic actions would unlock the more powerful actions which are necessary to deal with damage mechanics, instead of those skills being ready to use whenever. For example: Cure III, Medica and Medica II only hit party members who have Regen on them, and the MP cost and potency of Regen are reduced to compensate for this change. Another example: instead of reducing cooldowns, Lilies would increase the potencies of Medica, Medica II, Assize and Cure III up to what they are now and without Lilies those skills would not heal much.
Combining both of my suggestions would lead to the healer being very busy with healing in order to survive some mechanics. If encounters had some form of persistent damage aside from boss auto attacks, then continuously healing the party with single target heals would feel more satisfying because the healing wouldn't be wasted. It is possible to add dps spells to mix as well and perhaps create a new healer whose dps spells enhance its healing.