One thing you've also missed out in your diagram is the centrifugal switch shown in the picture of the stator coils, this opens the start winding when the motor reaches 75-80% of full load speed, ie: the start winding is never permanently energised.
That's in motors for applications that require high starting torque (refrigeration compressors, stationary power tools, etc.). Motors used in small-to-mid-sized fans are instead designed with the capacitor permanently in-circuit. (
https://en.wikipedia.org/wiki/AC_motor#Permanent-split_capacitor_motor)
It would also become very complicated (to say the least) to set a starting switch for 3 different speeds (ignoring the lowest speed on this fan, as noted before). And a 50uF capacitor rated for 400VAC or more across it
continuously would become very bulky and expensive, I would imagine...
