A belt driven system is possible but not seen for several reasons.
An acme screw driven stepper motor has a large mechanical advantage over the build plate meaning the torque required is fairly low. The trade off is that more rotations are required to move the same distance, this is advantageous in this case though because it means the resolution is increased. Removing this mechanical advantage by going with a z belt drive reduces both resolution of the movement and increases the required torque from the motors, neither of which are a good thing.
Another issue that is seen in a belt driven set up is a constant torque is needed to hold a belt driven Z in position, the belt driven Z is constantly fighting gravity. Compounding this problem, as more material is placed onto the bed the required torque to keep the bed in position goes up. This torque is not needed on a screw driven z axis since the z axis has sufficient internal friction to keep the bed in place even with the stepper is shut off.
