That sounds interesting. Kind of like filling up a fever gauage in rhythm games, in effect turning each fight into a mini-game. A feedback system that acts as positive reinforcement for people to improve. "How do I fill my fever guage? What rotation fills it faster?"
Then over the course of the dungeon, maintaining fever status could grant some benefit, like extra tomestones each boss, or extra gil, chance to gain an extra personal coffer after each boss that may contain stuff like relevant crafting materials and minions etc.
A visual feedback that shows players they have room to improve is a very effective incentive for improvement.