Hmmm, Kyrill, I'm not sure I want to go there!! You and Andy have said it all!
In truth, any power source, AC, DC or swings both ways, will have a source resistance, or impedance. A heavy current draw will certainly drop the line voltage, and yes, electric motors turning on will certainly dim the lights.
Line voltage sag is modified at the DC end of a power amplifier by the configuration of the transformer(s) and power capacitors, and of course the current demand of the amplifier, which is highly variable, literally in phase-shifted step with the music. You can see I'm painting a picture of some complexity here.......
Just as the primary of a trafo 'sees' the secondary of the same trafo, then so this works in reverse; this is not a mirror, but a window. However, the source resistance of the mains is around an ohm, though complex of course, so the glimpse the secondary catches of the primary is fleeting as 1R is very low and it can't see too much. If we use two trafos, one for each channel, then the view each has of the mains is identical, and the impedance so low that cross talk becomes almost indetectable. This does manifest as superior channel separation; I've done tests with single versus dual supplies and the evidence is very clear.
Further, the size of the filter cap bank is also significant, since the higher it is, the less the amp 'sees' the primary; it only sees the filter caps, and to an extent, the rectifier and the secondary. There is also the matter of the source impedance of the bridge rectifier and the caps, which is complex and discontinuous and very strongly influenced by the quality of both.
To my thinking and in my experience there is not much to be gained on the primary side. The benefits are gained with the choice of rectifiers and filter caps, and maybe to a minor extent the power trafo. I have witnessed A/B blind tests across a sample of 6 audiophiles with very different transformers and the differences are almost indetectable between double C cores v. toroids of the same capacity. In fact, no one person could reliably pick the difference. This leads me to believe that the primary determinants in the 'sound' of the power supply come neither from the transformer nor the mains nor the power cabling, but rather the rectifiers and filter caps.
Of course, this is just one man's opinion, YMMV, I could well be wrong, and lots of people are cleverer than I am, etc etc.... This is partially, anecdotally substantiated OPINION, and if I stand under a pyramid surrounded by citrate crystals with rhinestones and razors on the floor I could well think differently. I am aware that there are whole religions (and marketing strategies!) founded on these interested precepts, and I won't fight, disagree, or otherwise cause angst to anyone. We are talking here about what people HEAR, and this is psycho-acoustically subjective, and this should be stressed again and again.
This may not help, Kyrill, but we all live in hope........
Cheers,
Hugh