As someone who does design electronics for a living, the mains cable is not something that should ever be considered important. If it is, then the device you are designing is a decidedly 'fragile' device. Real engineers are aware that the vulnerable points in any electronic design are the inputs and outputs that interface with the real world. The aim should always be to
(a) protect these against potentially destructive signals (short circuits to ground or power, electrostatic discharge)
(b) condition against noise and radio frequency interference (into and out of the equipment)
(c) ensure stable operation for all legitimate sources/loads.
It is clear reading these forums that many boutique 'hi fi' devices do not meet these criteria, whether it is reputedly jitter-intolerant DACs, or amplifiers that can be destroyed by connection to an awkward load or short circuit. Sensitivity to the choice of mains cable (assuming it has adequate current carrying capability) would be another prime example - if it actually existed: it is hard to see how you could actually do this. I see two choices: either it is a case of expectation bias, or the amplifier has been designed extremely badly.
The point about the hundreds of miles of cable finally reaching your home is, of course, perfectly valid. The point about the final metre of mains cable being a restriction that could impede the flow is neither here nor there. If this was the case, all we would need to ensure was that our mains cable was equal to, or beefier than, the tens of feet of twin-and-earth that exist in our homes prior to emerging from the wall. A 100 metre reel costs a few tens of dollars.
Edit: it would be interesting to ask an amplifier designer what the ideal mains cable should be. If the answer was anything but "beefy" or words to that effect, we could then go on to ask him what the ideal R,L and C the cable should possess. If he actually had an answer for that, we could (a) ask him why he didn't mention this in the user manual, thereby risking his amplifier sounding worse than it could, (b) ask him why he didn't build the mains impedance matching into the amp, and (c) we could specifically design a cable costing $5 to achieve those exact specifications - obviously beyond a mere amplifier designer's capabilities - and maybe manufacture it and sell it to the amplifier designer to bundle it in with the amplifier! If R,L and C didn't cover it, that would mean there was something so mysterious about the required cable that even the designer of the amplifier didn't know about it. What chance is there of any of this working satisfactorily then?! The cable 'designer' doesn't know what the amplifier needs, and the amplifier designer doesn't know what the best cable should be. It is ridiculous. Occam's Razor says that audiophile mains cables are simply a triumph of marketing over common sense.