No answer to my question yet, I duly note.The industry does not pay attention to absolute phase. As a result, 50% of all recordings might be incorrect phase. The problem you have thought is that about 99.3% of all recordings employ more than two mics, often with tracks recorded in entirely different rooms. Sometimes these tracks are in phase with the rest of the project and sometimes they are not. This can result in out of phase bass which requires in some cases a special processor when mastering LPs. Otherwise the stylus can get knocked out of the groove. This does not happen with digital of course, but the point is that there are a lot of recordings that really are not absolutely in phase or out of phase.
Because of these factors inverting the phase is often not audible. You need a purist recording; everything has to be right in order to hear it. We included the phase inversion switch on our preamps on account of the fact that its a real pain in the rear to reverse the phase at the speaker terminals for each recording!