Why is the air gap between the stator and rotor on a motor kept as small as it is?
Air has a much higher reluctance (the magnetic equivalent of resistance) than the magnetic materials used in the motor. The smaller the air gap is, the lower that reluctance, and thus the higher the magnetic flux (which is the magnetic analog of current), allowing the motor to work more efficiently and at a higher power.

Smaller air gaps also minimize leakage flux, which means more of the flux that is produced actually does something, rather than just going through the air and doing nothing to help the motor work.