I'm asking this because the smaller the distances between electromagnets, the stronger the electromagnetic field.
I don't know if this would mean a proportional increase in power, be it either torque or RPM.
The closest I could find to this was this article which explores the use of ferrofluids to reduce the gap. It was able to double the torque, but nothing in a proportional sense.
For a constant field in the gap, the motor armature and running characteristics are independent of the size of the gap.
However, to get that constant field, a wound motor needs excitation current more or less proportional to the gap, so the gap affects efficiency. A permanent magnet motor needs magnet strength proportional to the gap, so the gap affects cost.
If the gap is already running at the maximum flux it can, so the pole piece material is at saturation, then reducing the gap further will not increase the field or armature efficiency. It will however reduce the MMF required to maintain that field.
Achieving a very small gap needs high mechanical precision, which is expensive. It's therefore a reasonable tradeoff for the manufacturer to aim for a larger gap, and spend more on magnetic field and less on mechanical precision, when trying to cost-optimise a motor. A larger gap also means slightly less 'windage' loss, from shearing the air in the gaps.
Reducing the air gap in a motor can only be taken up to a certain point. If the air-gap is too small there is a possibility that the rotor will hit the stator and, of course, this is to be avoided.
However, the benefits of a small gap are a lower magnetization current for the flux density needed. This improves power factor and reduces electrical power losses.
On the other hand, a bigger gap will require a larger magnetization current and, this in turn implies fringing fields (not coupling to the rotor). This means a higher leaker inductance. A higher leakage inductance means poorer torque at higher mechanical loading. This means lower mechanical power output.
But you still have to be greatly concerned about having a big-enough gap to avoid problems of the rotor hitting the stator.
It's the same for a regular AC transformer; more gap means poorer magnetic coupling equals poorer output regulation.
At some point the gap will no longer dominate the total reluctance of the magnetic circuit you you'll get diminishing returns. Otherwise you'd be approaching infinite torque with zero gap, which is not going to happen any more than magnets which come into contact are inseparable.
Things like manufacturing tolerances and bearing runout (new and at end of life) will limit how narrow the gap can be made, in any case.
