What then is the purpose of phase inversion switches on some DACs and Preamps - is that related more to things down the chain, like things going on with the speakers?
To invert the signal of one or both channel signals.
Invert one channel
To correct a polarity error in one channel or to play with.
(I have a cheap 3-CD set of piano where one channel is inverted throughout. If I play it, I need to invert one channel, otherwise it sounds terribly wrong)
If the channels are combined, after inverting one, some (stereo source) or all (mono source) of the signal may be cancelled (null test).
In a stereo recording, combined to mono, a signal panned dead center can (to a large degree) be eliminated - think "vocal remover" if you want to sing along and not hear the original vocalist.
Gives a funky sense of stereo expansion or other possibly amusing effect.
Invert both channelsTo correct polarity of the signal when you think it makes a difference whether it is coming out of the speakers inverted relative to the source waveform or not. Some gear (inverting) will "invert" the signal it receives. Other gear will not (non-inverting)
If the signal at the source is positive (microphone diaphragm compressed), the speaker driver should, at that instant, be moving toward the listener, in the process of creating a pressure (rather than a rarefaction). This leads to the question of signal inversion at the microphone, though.
---Audacity will permit you to play with channel inversion if you want to experiment and you don't have mono or phase (inversion) switches to fondle.
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A discussion - https://www.stereophile.com/content/listening-tests-and-absolute-phase
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