I think that lots of people have wondered about the why of the square root of 3 in three phase systems. The particular issue of the 'missing' 32V came up in a discussion several years ago, about the 'oregon fudge factor'.
Here I disagree with you.
I specifically brought up power factor and showed an extreme case where something is lost by having two coils, not in phase, feed a single phase load. What is lost _must_ be understood in terms of the power factor of the loads on the individual coils. And I absolutely agree: if you connect a single phase load to two legs of a wye system, because of the power factor seen by the individual coils, the equipment will need to have larger VA capability than if the coils were in phase.
But once you understand that this 'loss of capability' is created by power factor in the individual coils, you will see two other important points:
1) You see the exact same loss of capacity in a delta system. In a delta system the output voltage is the coil voltage, so no voltage is 'lost'. But add up the _currents_ in the various coils. You will see the exact same percentage loss of total current versus coil currents. In a wye system the voltage is lower than the sum of the individual coil voltages, but terminal current equals coil current. In a delta system the voltage is the coil voltage, but the terminal current is less than the sum of the coil currents. (In both cases the 'deficit' is explained using a vector sum.)
2) If, rather than considering single phase loading, you consider three phase loading, when you have a balanced three phase load then nothing is lost, and the power factors in the coils is the same as the power factor of the load. With a balanced three phase load a balanced three phase source doesn't create any additional 'coil power factors'.
-Jon