I can partially agree with the people who aren’t into measurements. My agreement is that we don’t always know what a good measurement should look like. But here’s what I firmly believe. If an audible change has happened, that change will be measurable. All it takes is some effort. We don’t have god-like hearing. Test equipment is orders of magnitude more sensitive to subtle changes in the signal. No change that we can hear is going to get past the equipment. If an audible change has occurred because of cable burn-in, that will be easily measurable by a competent person with decent equipment.
I recently tested a group of integrated amplifiers and thought I was hearing differences. I took out the calibrated mic. and compared the speaker measurements with the different amps hooked up. The frequency response showed very clear and repeatable differences depending on which amp was hooked up. I'm not all that competent, nor is my measuring equipment anything special, and yet even I could demonstrate measurable differences in the response of my speakers with different integrated amps installed. If I heard differences between cables, I'm sure I could measure that too.