Dedicated 20 amp circuit - Electrician laughed!

The Electrician would have a point if reproducing music was equivalent to running an electric fan... A steady continuous current draw. The flaw in his argument can be summed up in one word. "Transients". A transient response is the factor that defines the excitement and immediacy of music... The attack of a snare or blast of brass, the power and agility of an amplifier to faithfully reproduce a notes colour or character at low frequency. A transient spike requires a current spike, ergo, restricting current restricts transients. If your thing is listening to sin wave signals through your system, then it's not an issue. If you listen to music, then open up the current supply as much as possible. That is why replacing at least the bottleneck of the jug cord your amp came with, even with a budget, glorified jug cord, can make a significant difference.
I don't see the necessity of driving in a 2nd earth rod but running a 20A cable and fuse for your system should be a relatively cheap exercise and well worth a punt.

It appears as if your Electrician is not familiar with mission critical installations.
I wonder if he would have laughed if you told him you were going to be running a computer that required a 99999  reliability rating.

There are many electricians out there however, they all don't have the same level of experience!

I am going to call BS on this, or at least poor measurement. A 10 foot long 18awg cord at 15 amps (well over rated current) would be about 2.5V. A much more typical connection for 15A would be 14awg, and say 6 feet or about a 0.6V drop and 9 watts if running flat out. Even class-A amps at 140W would not draw 15A. If you had 40w of losses, either your cable or outlet is going to get quite warm.

AC voltage drop is the voltage dropped from the wall to the input of the equipment in use. I’ve measured a loss of 40 watts on an amp that makes 140 watts, so no-one should be surprised that that might be audible as well. I used a 3 1/2 digit DVM to measure the voltage drop and it showed around 3 volts. This was a pretty standard but inexpensive Belden cord. A more expensive Belden cord with heavier gauge showed a lessor drop and more power out of the amp. So no mystery here.

Can't agree with this either. The main limitation in high frequency power delivery is not going to be the AC cord from the wall, but the power transformer either in the equipment or outside your house.  Add resistance (or inductance) in series and you are going to soften those diode switching spikes and reduce the output noise of the power supply at high frequencies which is likely to be a bigger issue for most supplies than low frequencies which feedback can usually negate. There is a reason why Pass amps and other good quality amplifiers have inductance to slow down current delivery into the power supply. If you have enough capacitance and are not nearing the voltage peak of your amps in operation, I would guarantee most amplifiers have less distortion with a bit of resistance/inductance on the line.

If the power cord limits current during this period, the performance of the circuit using the power supply might suffer, possibly due to increased IMD since the DC might have a bit more of a sawtooth on it than if the current was not limited.

Where the dedicated line mainly comes in is noise rejection from other things that could be on the line and to prevent signal injection via a case ground voltage that varies in potential to signal ground with the draw on the AC line.