Any mains supplied electronic equipment should have sufficient internal storage to handle the peaks in the music regardless of the cord or line that is feeding it. The power supply has a time constant where it can continue to supply power even after the mains connection is removed. If you are going to use the equipment for continuous sine wave testing, yes, then the demands on the mains supply are great and all the connections are important.
With music, the crest factors greatly mitigate the average power required from the mains. You have high current demands when the kick drum slams but after that the demand decreases allowing the mains to recharge the supply. In that case, the internal supply provides the necessary peak power and the capacitors recharge between the peaks at a lower average rate. In fact, if you have a very large storage capacity in the power supply, any impedance in the mains helps to decrease the magnitude of the peak current surges in the mains as the supply caps are recharged and the mains current rate gets closer to the average rather than the peaks.
The downside of a well designed high storage capacity supply is that you have a high initial charge time constant. I used to work on a high power commercial electronic flash unit that had an energy storage capacity of 40,000 joules. It used a phase control circuit to prevent damaging charge currents when switched on. Once charged the current dropped to a very low value and only the leakage currents of the oil filled capacitors plus any control circuitry were reflected to the mains. When the flashtubes were fired, they would essentially short out the capacitors for period of a few milliseconds and then the phase control circuit would again mitigate charge current until the bank was fully charged.
An amplifier will hopefully never short out the power supply. If it does, you have other problems. With an amp, if the supply is large enough, the time constant of the load during the peaks is sufficiently long enough that the supply will not sag very much. Think of it as an RC (or RL if a choke supply) time constant where the R is the speaker and the C is the total capacitance of the supply. To prove a point, lets assume the supply was really mongo and had 100 farads of capacitance. The time constant for an 8 ohm speaker load would be 800 seconds. It could supply the current to the kick drum with virtually no drop. The time to totally recharge the caps would be longer than if you had a very small storage capacity but the good thing would be that the supply voltage would not change much or very rapidly.
So it really boils down to having a good supply in the equipment. The higher the capacity in the supply the more the equipment acts like it is battery operated and only relies on the line for recharging. If you had a battery operated preamp for example that took 24 hours to recharge you could probably recharge it from a small wall wart power supply. The capability of the mains as far as the ultimate operation of the preamp would be totally immaterial as long as it could supply sufficient power to recharge the batteries during the charge cycle.
So I have always concentrated on the power supplies in the equipment I have either built of bought. If I purchased a unit with a weak supply I fixed the supply rather than trying to fix the mains. Regardless of what you do with the mains you can only go as far as the utility supply to your meter. All the many things that happen to mains power are in the domain of the utility. A well designed power supply will thumb its nose at any mains problem because the time constants are so long in relationship to the waveforms you will encounter in music. Whew, more than enough said. How do you think I really feel about this issue?
