Frantz,
That is what it is supposed to do. Again, respectfully, I am not debating your position. I am thinking out loud about how one might answer the original question which is the title of this thread. I am saying that such a test
might show if not just the power cord but any part of the power supply be it a resistor, diode, capacitor or even hook up wire could impact the audio circuit's sonics. Within this broadened context, I really don't see it as a Mosquito/Abrams situation. The test is not on the cord but on the amplifier. The cord just happens to be one of the easily considered variables. Given the current set of metrics for quality control, none to my knowledge have ever mapped out performance under dynamic conditions. Very different from say the automotive and aeronautics industries where say engines are mapped out with factors such as air pressure and temperature and aerodynamics are subjected to varying velocities and directions. All I've seen from the audio industry are averages at static conditions or very few full bandwidth conditions but with limited predetermined amplitudes and limited durations.
By introducing frequency and duration all we're doing is filling in the blanks but again a composite of tones do not a real world test make. Like air velocity and direction for a wing, an amplifier must deal with ever changing conditions represented by the loudspeaker's back emf. We already know what the benefits of a stiff power supply are. We already know that subjectively some people prefer underdamping rather than optimum or maximum possible driver control. What we'd be doing is mapping out performance in the frequency and amplitude/time domain. For example, we might be able to see not just at what power output thermal distortion begins to set in but exactly what frequencies are impacted. Such data could be very useful for a designer.
Going back to the power cord, the very same argument is used against speaker cable. Even you prescribe that at 6gauge all things are equal. At least you have a standard, a rather high one since 6 guage is not exactly in stock like 14 gauge is. Now supposing such a test carried out independently proves that 5 feet does change performance in the audio circuit that it feeds, could the methodology and results not lead to the design and construction of a low cost power cable that has minimum impact on an audio circuit? I say why not? Could this, if it even works at all, not bring down r&d costs that will ultimately benefit the consumer? If so then again why not? Dynamic testing has kept us in the air. That it turns out that they forgot to fire 300mph frozen chickens into engines and cockpits with a cannons to avert the consequences of bird strikes, is beside the point!
I say why not keep an open mind about things. To lighten things up a bit, if an archeologist found the fossils of a modern cow in rock strata with an age that no cow had supposedly existed yet, the immediate reaction of the scientific community would be that it was a hoax. Conspiracy theorists would say that the U.S. Government has a time machine recovered from the crash at Area 51. Cultists would say that indeed Cows are holy and that it is a sign that the world is ending. A real scientist however would not be dismissive but rather would try and find out simply how that cow got there despite being able to trick all the dating protocols. If all goes well, the world ends up with an even more accurate dating method if not, conspiracy theorists and cultists will unite saying that the US Government has a time machine and has been transporting holy cows into the past to avert the end of the world. Meanwhile, the scientific community will put the remains of 3 million year old bessie in a drawer never to be seen again probably to hide the fact that either darwin was wrong or a farm hand got the better of them.
I don't think I'm being unreasonable. I gave a simple, highly possible, potentially useful, practical and impartial way to answer the question. Some apparent evidence of that impartiality is I'm getting it from both sides of the fence.