All of my characters at some point in the game are capable of casting both Cure and Cura at the least.

Try giving everyone Cura, but only certain people should use it in "emergencies", like your tanks.

Also:

oh and i use vaan as my leader, i don't use gambits with him, i just treat him like a character from the older turn based final fantasies mashing square when i get to an enemy, choosing steal, then attacking or healing/ curing ailments when needed.
Try setting Vaan's gambits to do this, and control your white mage.