you make an interesting point. I read a piece by Harry Pearson (RIP) in the Absolute Sound decades ago where he basically said that there are unexplainable truths/realities in Audio reproduction due to the limitations of our scientific knowledge. He asked the question about whether we, audiophile hobbyists, felt that science had/has ALL the answers at this point. He obviously felt it didn't. While, to this day, I'm still undecided I'll admit that he's still got me wondering!;)
I actually believe differences from our listening experience can be measured, but our hearing is very complicated and it's hard to devise a measurement technique.
In the case of cable burn in, it can be measured, but you need very sophisticated equipment which can cost a lot of money and it's not like it's a survival matter so people don't trouble doing it. If they can hear the difference and it can be explained by basic physics then it's good enough for them.
Even if you have the equipment, you need to have extensive knowledge in physics and electrical engineering so it's not like push a button kind of thing. I once saw a website that measure jitter on a bunch of DAC and concluded that cables don't matter. I mean it's like comparing difference cars using 0-60 number. Our hearing is much more sophisticated that can be measured by some basic parameters.