Someone please correct me if I’m wrong, but two sources having inverted polarity can result in sound cancellation when the two sources are mixed. Inverting polarity is a simple process in post, but as an additional process it can degrade audio quality.
You're correct on the first part, that mixing two similar signals with one having inverted polarity CAN result in sound cancellation.
You're also correct that inverting polarity in post is simple.
I would quibble, however, with the notion that the additional process would degrade signal quality in any way. If it's done in the digital domain, then it's just math, and rather simple math at that, to invert a waveform of a digital file. On the other hand, if it's done in the analog realm, it could be implemented by a flip of a switch or a cross-wired cable with no particular degradation. But yeah, if you did another pass from analog tape to analog tape just to invert a signal? Sure, that would cause degradation, but I don't think that applies to this situation.
Thanks for letting me nitpick, and while we're at it, please note that polarity, and not "phase" is the correct term for that which is upside down but not time-shifted. Phase would involve a time-shift, and not just a hot/cold switcheroo!