Sure, hypothetically, we could do this.
Barbarians had abilities that lasted until the end of the encounter. I'd propose not to simply steal the
4e at-will/encounter/daily dynamic, though. Come up with something a wee bit different that can still use the structure of existing powers.
My recommendation? Label powers as basic, advanced, and heroic.
You can use basic powers as a standard action.
You can only use one advanced power per encounter.
You can only use one heroic power per day.
As you gain levels, you learn more powers of the different types, and you gain the ability to use more advanced powers per encounter and more heroic powers per day. Unlike
4e, I wouldn't limit a high-level character to only using each daily power once per day; rather, give a limit to how many such powers you can use each day, but let the person use the same power multiple times if he wants.
That is eminently derivable from wizard spellcasting.
Finally, I'd add some mechanic that lets you recharge your advanced and heroic slots. Make it work sort of like 'super move' meters in fighting games, or limit breaks. If you reach a certain threshold in the course of a single encounter, you get caught up in the action and are able to pull off more acts of derring-do.