In that light, the typical designer generally strives for ’listenability’, that polite, acceptable presentation, which is quite often not what the microphone ’heard’ or the recording stream produced. (Deeper discussion deferred that many ’modern’ recordings invert various polarities to ’fill the mix’.) But I am addressing the speaker reproducing its input signal. Wilson (as example) inverts polarity at each driver exchange (crossover point.) Good engineering executes the hand-off between drivers with smooth phase transitions. The absence of abrupt glitches gives the ear-brain no hard evidence of trouble. And most design styles, companies and critics call that victory.
In contrast Jim Thiel, Richard Vandersteen (and a few other oddballs) chose to preserve the phase-time information intact. Many of you guys appreciate that, most people do not. When phase is kept intact AND the drivers are aligned so that their leading edge transients all reach the ear simultaneously (time-alignment), we call that Coherence. I notice that today the C word usually means ’smooth phase transitions’. rather than our assignment of ’integrated waveform’ period. First order roll-offs (including electrical and acoustic elements) sum to produce zero phase shift. (One driver leads by the same amount that the other lags, such that at the design listening distance, they sum to produce no shift.) Add physically equidistant sound sources, and you get an actual representation of the input signal representing the recorded sound, with no need for the brain to descramble the phase and time information. Thiel and Vandersteen decided that goal of authenticity was worth all the difficulty of making it right. The industry at large does not consider that element of fidelity to be important, or important enough to warrant its difficulties.
I suggest pulling out ’phase’, ’polarity’ and ’time’ in trying to understand the landscape. Richard Hardesty’s journal has been cited here. I consider his clarity and teaching style to be stellar.