Polarity of speaker drivers

glai, your basic assumption of why switching a drivers polarity is correct.
It has everything to do with phasing.... There is no speaker with a crossover that is completely phase coherent.... period. Even the most "Phase Coherent" speakers have phasing issues.
We normally talk about crossovers typically in Electrical slopes... we may call it 6db per octave or 12db per octave, but when you add the natural rolloff of a driver along with phasing, in the end a 6db slope may be 9 or 10 db per octave.... I often might use a 18db per octave electrical slope on a tweeter and a 12db per octave slope on a woofer...On my last pair pair of speakers,  the end result was a 24db per octave roll off and the crossover point being 6db down. This combination rolls phasing around to come back in alignment and in fact, quite often in closer alignment than using what most consider the only truly phase coherent 6db slopes. When you listen to a pair of speakers and the polarity is crossed on a speaker,  most folks do not say that the speakers polarity is wrong,  they say "The Speaker is out of Phase".... When you switch the polarity, phasing comes back in alignment.
Under Electrical crossover conditions, when you cross a tweeter and midrange at 12db per octave slopes, they are 180 degrees out of phase, the idea of switching the polarity of 1 driver is an attempt to improve phasing or bring the drivers back in phase with each other. Anytime the polarity is switched on a driver,  this should be the reasoning behind it. 
This is a very elementary explanation. I hope that it helps.  Tim

I put together a speaker kit, the LM-1, and posted the simulation files so you can play with crossover design yourself. This may help you get a better understanding of polarity and phase relationships.

https://forum.audiogon.com/discussions/try-your-hand-at-crossover-design-free

Best,


Erik

Having jumped into a two channel system head first I took the advice of some very experienced audio experts and went with what I felt were the speakers with the fewest crossover/phase issues that would deliver the audio signal across the entire frequency range. 
As Tim has stated, there are ways to bring drivers back into phase and the really good speaker manufacturers do this with aplomb, I'm sure. But you still have notches in critical areas of the frequency response as well as crossover inefficiency and IM distortion as the crossovers heat up. 
Active crossovers that sit outside the speaker and are placed between the preamp and the amps with the amps wired directly to the drivers had some appeal and serve as answers to the above problems, but all in all the simple full range driver with first order crossovers to the tweeters and built in subs had appeal in many facets. Coherence in a speaker is a pretty strong quality. 
JMO, but any move toward straight wire with gain is a plus. Full range drivers have their issues as well but phase/polarity isn't one of them. Actually the immediacy of the sound is startling at first, becomes endearing with time.

Well, I think that trying to divine what speakers will sound better or worse based on crossover complexity is very difficult indeed.

While I have my own preferences for drivers, and crossover components, I would always let my ears listen before worrying about the technology. Same with DAC chips. Implementation and total system synergy matters mroe to me than statistical evaluation of components.

My LM-1 Kit has a single cap and 1 resistor on the way to the tweeter by the way, with only 9 crossover components in total. The woofer has only 1 coil on series, and has fantastic phase integration between the two drivers.

Best,

Erik