So, if you parallel a mess
of capacitors to make a run capacitor with the correct value for PF=1,
then the capacitors will dissipate zero power.


not true.
if there is current flowing through the cap, ESR of the cap will dissipate power.
The purpose of a motor cap is not to correct the PF.

There is no such thing as a single phase motor.
Small motors have shaded poles or other tricks to create a phase shift.
Medium size motors motors use a cap.
Large motors are typically fed with 3 phase.

I think the optimum cap value, is where the current through the aux winding is 90 deg out of phase with the main winding.

m