Yeah, you can cause it to short cycle for sure. But you can also get better control without excessive short cycling. If you're worried about short cycling, just include that in the control algorithm.

Short cycling would be bad in the sense that the motor frequently turns on. The maximum current is during motor start and the maximum motor coil cooling is when the fan is running at high speed steadily. So if it starts a lot and doesn't run much at high speed you might tend to overheat, sure. That would definitely drastically reduce the motor lifespan.

If you are still starting periodically and running for awhile, you can see where this goes.

I think it's not overshoot/undershoot that is happening so much as delayed kick on.