but I think we can state pretty unequivocally that the goal of the power supply is to isolate the output (audio) from the input as best as possible.I would disagree with that statement. There is really no "isolation". They are all related.
Technically the diodes in the power supply perform a modulation function on the incoming AC which is why you get DC.I think that is called "rectificatioin", not "modulation".
With regard to the "Audioholics" vid, I actually agree with most of what he said on his other videos, but he probably is wrong with respect to power cable.