If they want to keep some form of battle high, I'd make it more like a rage mode.
You could build it for fighting, and build it even faster for assisting or killing, until eventually you get to go super-saiyan mode, doing like 1.5x damage, it would only last a minute or two. But if you disengaged from battle, it would fall off in half that time. If you were building it and stopped, those gains would quickly decay as well.

This way you could get rewarded, even if you're just trying to stay in the fight- that push would build some momentum. It would reward offense and punish disengagement.
Most importantly! It shouldn't increase healing!