Skin effect isn't a religious phenomenon, it's an electrical engineering concept describing how AC current travels on the surface of a conductor to a depth with varies with frequency, which is well studied, and easy to measure, and model. This is taught to engineers in the same dry and uncontroversial way as ohm's law or any other basic concept. If you want to measure skin effect at audio frequencies, all you need is an audio frequency generator, a precision resistor, a length of the cable you're trying to measure, and a wide band AC volt meter.
The table below gives some examples of skin depth at different frequencies.
Skin depth in copper
Frequency Skin depth (μm)
50 Hz 9220
60 Hz 8420
10 kHz 652
100 kHz 206
1 MHz 65.2
10 MHz 20.6
100 MHz 6.52
1 GHz 2.06
So note from above, that #14AWG, with a radius of about 0.8mm or 800um will already be exhibiting some skin effect at 10kHz, and will have increased resistance by 20kHz relative to its DC resistance.
At powerline frequencies you need a huge cable to start seeing skin effect,At 60Hz you would need a conductor diameter of greater than 16mm!