One of our A320 simulators has no hydraulics. When you think about how much a simulator bounces around, I'm sure there are electric motors strong and quick enough to power flight controls. I suppose the problems are weight, reliability, wiring, generator loading and so on.
On a side note, my understanding is that airbus flight controls are not balanced. Saves weight not having to carry all that depleted uranium around in your flight controls but what happens when all the hydraulic fluid has drained. I know there is no manual reversion, but does flutter become a major issue? I know the flight controls have a damping mode but does this require fluid in the lines or is it something within the actuator itself?