The first point is that my assumption of smoothing by the capacitors is weak. There is always ripple, a saw tooth shaped variation in the DC (not quite) voltage, and sharp current transient spikes replenishing the energy stored in the caps. These spikes are comprised of high frequency components, producing corresponding distorting voltages, which may not be effectively handled (filtered) by the large filter caps which are not ideal and function as intended for low frequencies only. These high frequency signals then bleed through the caps and can then be reflected back and forth between the power source and the amplifier circuitry based on transmission theory. This doesn’t even address the potential noise generated in digital systems that will appear on the signal and power bus of a system. Perhaps power chords and line-conditioning affects these also?
Our problem is that we distill a technical problem down to a simple ohm’s law based steady state small-signal analysis. In reality, power connections are inherently a large signal transient analysis problem which could be analyzed but aren’t. Bottom line is that many of us learn Ohm’s law and think we understand everything and we try to simplify/distill a problem down to fit our analysis abilities. Ironically, I don’t believe that many of the cable producers have great technical insight, but rather, they have a practical insight into what seems to work.