Inescapable logical conclusions have been proven wrong on so many occasions in the world of science, you push, it moves forward is no longer an inescapable logical conclusion.
A bad scientist makes such a claim without testing being carried out, it's your personal view, as it is with a couple of others here, no one has tested out this theory.
Until they do, it's a cop out & a convenient get out clause, that's my personal opinion until proven wrong.
Its not an opinion its a fact. If the amp is noticeably affected negatively by the tiny possible difference that a mains cable could cause to the mains conditions then it is defficient in the area of psu, psrr and emc.
It is a design requirement to cope with varying mains conditions as this is guaranteed to be the case in every installation. There is guarenteed to be a varying level of voltage, waveform distortion and electromagnetic/ RF noise.
To convince yourself that it is anything else but a deficiency is delusional.
The test is that you (and others) adamantly claim that their amps are affected by mains cables. If this is the case, and you and others will argue till the cows come home that it is, thenyour amp cannot cope with very subtly varying mains conditions without noticeable variations in performance. This is not a virtue.
It is so simple that its utterly mind boggling that some choose to argue against the point.
If we take one aspect of mains quality, and I will lump it under the broad banner of RF:
EMC regulations
The Directive requires that products must not emit unwanted electromagnetic pollution (interference) and must be immune to a normal level of interference.
In essence the requirements of the Directive are very simple - it basically states that products must not emit unwanted electromagnetic pollution (interference) and, because there is a certain amount of electromagnetic pollution in the environment, that products must be immune to a reasonable amount of interference
Before you argue about the definition of reasonable you should consider the following. If you are one those having issues in this area (abnormal levels of mains problems) then your choices are, buy a better designed amp, fit appropriate filters, or use a regen. A mains cable on its own is never a credible or effective solution to any of the mentioned problems.