Any piece of equipment with a well designed power supply only requires a power cable that can handle the current load. Increasing the gauge beyond that makes no difference. Dressing up the cable in a sock and adding good looking terminations and psychologically the system will sound better. Vision and hearing are hopelessly interconnected.
Having said that I stumbled into an exception. A friend related that he heard a cable make Sound Labs speakers sound better. He brought a pair to my house and in deed the cables actually worked. I ABed myself to death and sure enough fine details were more audible. On Waltz for Debby with the stock power cords the crowd noise in the background was audible but the speech was indeterminate. With the new cords I could clearly understand most of the background talk. The cord powers the very low tech high voltage power supply to the diaphragm. The power cord has some sort of filter in it. My guess is that noise in the AC is somehow interacting with the diaphragm to lower the signal to noise ratio. The speakers are powered indefinitely and at rest they are dead silent. The filter must be removing this noise that obviously is interacting with the audio signal.
This is an exception as the AC is being converted, amplified, to 5000 volts DC by a very basic power supply which is not regulated in any way. My guess is that the DC is being modulated by the "noise" and you would only notice this when a signal is applied to the speaker.