How about we just eliminate 'refreshing powers' altogether.
If you want to do something cool, you either build up momentum to pull it off, or you need to spend a lot of time.
I always wanted a magic system that had a bit of the vibe of Magic: the Gathering. You enter battle, and your fire wizard starts by spending an action to Gather Power. Fire swirls around her, dealing a bit of fire damage to anyone who enters or starts their turn in the area. Then the wizard has some fire mana, which she can spend to hurl a fireball. Some spells might cost no mana, but the good ones require you to build up to them. But you can't hold onto mana for more than a minute or so, or else it starts to burn you.
Or a fighter needs to warm up. He could have a rhythm meter, like in some fighting games, and each round he gets some points he can spend to improve his attacks, and certain 'fighting styles' give more points if he does certain actions. The Wuxia style would give bonuses if he attacks an enemy while jumping or otherwise not standing on the ground. The Knight style might give bonus points if he lets his opponent attack him first.