You can disagree but I get the impression you are not technically qualified to do any more than "disagree". No they are not "all related". A primary purpose of the power supply in an amplifier is to isolated completely the AC from its impact on the audio signal.
Rectification is the electrical function, modulation is the signal processing operation that occurs. The rectification is a signal processing multiplication function, or modulation. Ideally you would only modulate the 60Hz AC with only 60Hz to yield 0Hz = DC, but the modulation function ends up being something more akin to a pulse (rectangular waveform) multiplied by a sine wave, hence you end up with all kinds of harmonics of 120Hz that you need the capacitors to filter out. Ideally you design your power supply with inductive filters to extend that "pulse" and reduce those high frequency harmonics to there is less ripple for the capacitors to filter.
Rectification is the electrical function, modulation is the signal processing operation that occurs. The rectification is a signal processing multiplication function, or modulation. Ideally you would only modulate the 60Hz AC with only 60Hz to yield 0Hz = DC, but the modulation function ends up being something more akin to a pulse (rectangular waveform) multiplied by a sine wave, hence you end up with all kinds of harmonics of 120Hz that you need the capacitors to filter out. Ideally you design your power supply with inductive filters to extend that "pulse" and reduce those high frequency harmonics to there is less ripple for the capacitors to filter.
andy21,171 posts07-05-2020 10:28pmbut 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".