The way I see the possible causes of cable making a difference:
Quality of connection at both ends..tightness, contact area, oxidisation.
Microphonics.
The cable in close proximity to amplifying circuits, possibly picking up rfi from external sources or the transformer in the amp. Weave / sheilding / material may change the characteristics.
I don't see bad amp design to blame above.
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The problem with "blame" is that it depends on the circumstances, etc. I'd expect a designer/maker to try and ensure their amp worked OK over the range of mains voltages, shapes, and dc and earth returns, etc, specs the mains suppliers define as within their specs. And to cover a bit more than that for luck Ideally, cover what is typical for the bulk of homes. (The snag there being who surveys this and where are the stats?)
Connections: This isn't a cable issue as such but, yes, you want decent ohmic contacts. So plugs and sockets have to be well made, etc.
Microphonics: For *mains* cables this really should not be an issue. I'd be interested if anyone can show that thumping a mains cable in normal use produces a significant measurable change to the output of a well regarded amp in a normal setup.
Pickup of RFI: The snag with 'weaving' or 'twisting' is that for the same reason that this tends to reduce radiation being picked up it also tends to reduce any RF on the cables being radiated! So it may help one class of problem at the expense of increasing the risk of another.
To make sense of this people do need to make two mental distinctions about the assumed mechanisms when they talk about 'RFI'.
Firstly, having the 'RFI' guided *along* the cables is quite different to having them act as an antenna and gather it in from the surrounding fields.
Secondly: Treat LF as distinct from RF. Changes to the shape of the mains waveform when you look on a scope are largely due to things like the leading tops being shaved by current demand or chunks being eaten by PSUs. The bulk of this is at low frequencies which - apart from series resistance/inductance at LF - a cable won't alter much. (And if it has a high resistance/inductance at LF it will also *generate* this when the amp PSU takes chunks of current. So as with the above weave point, may make one problem worse to 'cure' another.)
The real RF is at higher frequenecies, but may cover a very wide range from neat audio up. So for reasons already discussed, finding a mains cable for this is coin tossing. Fine if you're lucky. But my view remains that for *RF*I a cheap filter is quicker, cheaper, and more reliable. Just look at the rejection specs of 10 quid filters. For *LF* garbage, if your amp dislikes it, then your mains may be so bad that you need a regenerator. Or a change of amp.