Phase Coherence is used in various ways by various people for various purposes.
I understand. I am personally got lost with all the different terminologies.
Very simple and very difficult!
Being working on DIY, it usually takes me much more time than a typical high order speaker. But still, I hope more speaker manufacturers will do it. It may be very difficult but not impossible.
I think it's just an "excuse" that most people won't try it.
I was thinking about how our hearing may not be so sensitive to high frequencies and the high freq. phase shift. In our normal environment, high freq. is very reflective and when sound reflects, its phase will get change as well. Also diffraction will cause delay in high freq. and phase shift as well. If human is sensitive to these, it would drive us crazy.
That's why our hearing is only sensitive to long delay, not short delay, and the long delay we hear is what we call "echo". Imagine if we listen to high order speaker and we hear all "echo", I guess that would not be very good :-)
But having said all that, I still think time-phase coherent could make a difference, and if I could, my speaker would be all time coherent.