Why doesn't AC motor slow down when connected in parallel to a capacitor?
During the zero point, no power from the source goes to the load and the capacitor is holding a charge, but not charging.


This is your misunderstanding.

Since the capacitor is directly across the mains with very low resistance anywhere in the circuit the capacitor voltage will follow the mains exactly in sync. There will be no lag (as there is in an RC circuit, for example) because there is no resistance.

The capacitor has no affect on the operation of the motor.