Power Cord Burn-In

You don't need to model "all facets of the musical experience and its impact on the human emotion" in order to model the effect a cable has on the signal passing through it. Of course, once you know the effect the cable has on the signal, you also need to know whether that effect is audible to humans. There's a good deal of scientific work (outside your field, of course) on the latter question, Dr. Morris. I recommend that you familiarize yourself with it.

Well of course it can't be correlated to measurements, since it happens inside your head. But you can't enjoy what you can't hear.

Actually, that's not true. You CAN enjoy what you can't hear. But in that case, your enjoyment is coming from something other than the sound of the component, so the technical parameters of the component are irrelevant.

When differences ARE audible, however, there is often a correlation between measurements and enjoyment.