Can you tell me which direction your eardrums are moving at a particular instant of time?

If not, then you don't give a damn about the input being inverted.

The whole issue is ridiculous; a total non-isuue.

There is no way to hear the difference!!!

But not all the time.  Closer to the truth is you CAN hear phase irregularity given a phase coherant recording.  I've heard it with my own ears.  Given that recording quality and system quality tend to go hand in hand, that is as your system improves, you tend to search out better recordings and or listen to the better recordings on your home rig and leave the other for your car or other system where quality isn't bothering you.  The best thing to do (I have a Lazarus Cascade Basic that does the same thing)  is to listen to  your best recordings, swapping the leads as needed.  When you find what you like, keep it.

Phase isn't hooey.  Period.  It matters, and once you get it right, you'll know it.  If you are using shielded speaker leads, make sure you are switching the leads at the speaker, in the event the shield is tied to earth.

This is why you play around with it.  Trust your ears.

The term "phase irregularity" is absolute nonsense! There is no such thing.In this context, something is either in phase or 180 degrees out of phase.

It is certainly true that all speakers in a system need to be in phase with each other, but the idea of "Absolute Phase" is total crap.

The idea that you can hear the difference when the microphone element at the recording venue moves one way or the other and that your speakers have to be in phase with it is the stupidest thing imaginable.

It might surprise you to know that the engineers at the recording venue and mastering lab do not take the trouble to preserve "Absolute Phase", so the whole concept breaks down right there.

There is no way to know what the "absolute phase" of the recording itself is, so trying to "maintain" it in your playback system is ridiculous and meaningless!!!!

Duhhhhhhh!