Is there any reason you couldn't use belts
You could, but just like a Z axis on a CNC router, you need to be careful that it does not free wheel down when power is removed. If it is light enough and the stepper detent torque is strong, you may not need to do anything. A weight on the return length of the belt could help. It would only need to be enough to augment the detent torque of the steppers.
Another thing I often thought about was having a relay switch one or more sets of motor coils into a direct short. That would significantly increase the off torque. On some portable CNC devices like a printer or little router, the X and Y can slide around in transit. I thought that shorting feature would nice passive brake on the system.