Power cord choice?

Your amp and/or power conditioners are designed to take the raw power, filter it, clean it, do all the other magic and then send the signal to your speakers.

Ok, firstly amplification has no “magic”. IOW, Gandalf plays no role here.
A power supply job is to rectify a 50-60Hz AC supply, rectify it and remove all ripple (read AC) from the DC output. 

An AC signal is not raw, nor is a DC signal cooked; Gordon Ramsey doesn’t play into amplification. Less noise on the AC source will ALWAYS result in less noise on the DC output from the power supply. ALWAYS and every time without exception.

The amplifier stage then receives the DC supply and makes a copy of the input signal using the DC supply, which end up going down the speaker cables. If the DC supply coming from the power supply is not perfectly ripple free, your sound is compromised.

How do we believe a 3 foot piece of cable, from the wall socket to the amp is going to change the sound coming out of the speakers?

Because the “3 foot” cable acts as a filter and reduces noise from the AC before it enters the the amplifier’s power supply. The cleaner the AC that enters the power supply, the cleaner the DC will be that it produces. The cleaner the DC, the better the sound.

The idea that a power cable won’t help, is pure ignorance. If you obtain understanding of how amplifiers work, it will become very clear why cables improve sound.

A good quality isolation transformer feeding sn audiophile grade power conditioner is the best you can ever do.

Not even close. The average Li battery with full sine wave inverter will blow any isolation transformer - power conditioner out the water at a significantly lower cost. 

Power cords are really pretty simple.
They are filters. If you can't hear any difference between power cords, you either are 1) blessed with pristine power, due principally to your location in the world, or 2) are cursed with some component(s) in your stereo that is such an underperformer that it masks the improvement the power cord brings.

3.) You're deaf.

I have $40,000 worth I have equipment all connected with AmazonXLR cords. It sounds amazing I have people over all the time that if they knew I used Amazon cards they wouldn’t believe it. This is not an ad for Amazon this is an argument against thousand dollar power cords add thousand dollar interconnects.

Your argument is not valid. Simply because you feel you spent a lot on your system does not diminish or change the experience I, or anybody else have had by swapping out cables.

I build my own amps. I spent more than 15 years refining my current amp to fit my environment and sound perfect to my ear. I have swapped out almost every capacitor and resister numerous times to achieve the sound I want. Money cannot buy you that. I know which power cord, interconnect and speaker cable combination works best with which particular combination of resistors and capacitors works best with which isolation platform works best with which power conditioner / battery combination works best with which type of source. 

No jokes, if a system like the one you have doesn’t exhibit noticeable differences in sound when you swap cables, you have issues which you should address.
(I don’t mean you personally, I mean your setup)

LOL!!! Posting videos from Ethan Winer and AmirM on cables is like posting articles from the anti vax crowd on the benefits of .... vaccines

Next he’s going to post videos of Stevie Wonder evaluating modern expressionism … 😂🤣

Deaf and delusional … 😂🤣