Using Smart Dimmer for Fan - why not?
To dim a light, you decrease the amount of power. That can be done by lowering voltage (works well with some things but not others) or limiting current or by only supplying power part of the time - e.g., by changing the waveform (as noted by Harper). Some of these same "tricks" work fine with motors, but generally speaking modern dimmers don't work well with motors - or rather, the motors don't work well with the dimmers. There actually have been issues even with some lights - many fluorescent and LED lights do not work with dimmers and it is always best to make sure that a light bulb (unless it is incandescent) is specifically designed/tested to work properly with dimmers.

How does the 5-speed fan switch do it? It may be variable voltage (e.g., different taps on a transformer) or current (some sort of limiting device) or some other method, but designed specifically to work with the fan motor. Dimmers for lights simply don't work the same way.

If a light dimmer does happen to work with a fan (or other motor), I would watch out for overheating and/or lower motor life.