BTW, I've never seen anyone contradict the belief that speakers have different distortion products moving forward vs. inward. Looking at the mechanics of a speaker (the surround is rolled one way, it can't have the same movement both directions, ditto the surround & voice coil) this becomes more obvious.
An old trick to cancel the above defined uneven polarity distortion components is "Isobarik" woofer loading, but w/ a twist. Isobarik mounts one woofer behind the other to cut the enclosure volume in half. A twist is to reverse the physical relationship of each driver (one's rear faces the other's front). The cones move in reverse directions vs. their chassis (though they are wired out of phase, so the sum result is in-phase). This entire exercise is absolutely pointless if speakers don't distort differently depending on their direction. BTW, it works very well, at least below 100 Hz. It's expense & mass are the only reasons it's not an audiophile standard for bass.
The above is the speaker world's answer to Bongiorno's full dual-differential full-complementary amplifier topology, the world standard for high end power amplifiers. The uneven distortion products are cancelled.
This may be one reason absolute polarity is audible, again, depending on the speakers. If the original transient of the original music waveform started out positive, inverting it is audible. The distortion component of the speaker is altered when its polarity is inverted.
Again, w/ non-in-phase speakers, the test is probably moot.
Manufacturer's who install polarity switches on components are not doing it because they ran out of stuff to worry about.