Pnumatics can be used, some British airplanes have used pnumatics. There are some advantages. If there's a small leak, you don't care. You don't have to have a return line.
On the other hand, if a line ruptures its' MUCH more exciting. Small high pressure air pumps are much harder to find. And there's all the stored up energy that you have to get rid of. If you have 3000 psi in a hydraulic line and you come to the end of the piston gear stroke, the pump turns off, the piston stops. If an air valve turns off, you still have 3000 pst trying to move the piston.
So it's POSSIBLE, but it puts you into more basic design.