Impact of phase inversion by preamp

some discs were inverted polarity relative to others

I only checked polarity between the reference pressings. I wanted to hear each with the same relative polarity.

As far as the mechanics, just plug a sampling scope into a tape output and check first impact. This also let me check max level and to a lesser degree compression if the wave shape was altered.

As mentioned, multitrack recording may have inconsistent polarity between tracks. I didn't record or mix the album, so I had no idea as to absolute polarity.

You seem to support my assertion that 50% of all recordings are in absolute polarity. Thus the need for a polarity (phase) switch.

I have no idea what %.

That some recordings sound better in one polarity flipped at the loudspeakers, no doubt.

Whether an upstream switch rather than speaker invert is better, I can't say. More convenient, definitely. Remote controlled, even better.

Today, I don't bother.

With regards to polarity in a multi way speaker with drivers wired out of phase to each other, my understanding is that this is done because for example the bass driver may have a second order crossover whereas the tweeter or mid driver may have a third order. You would wire one out of phase to the other so the and resulting sound would be all in phase.
Or if there is a physical distance difference to the voice coil one could be wired out of phase to the other again so the resulting music is coherently in phase when it reaches the listener.
So you should still try to observe correct polarity throughout the signal chain.Another thing to consider is older Jbl pro drivers have the black tab as the positive so some times could be inadvertently wired incorrectly

That’s real nice and everything but it’s not what we’re talking about.