Does Time alignment and Phase coherency make for a better loudspeaker?

It all depends on how the designer achieves T/P coherency. 

You cannot achieve T/P coherency with room treatments. 

i have modest specimens of 3 time-and-phase-aligned speakers -- one by magnapan, one by thiel, one by vandersteen, and they all image equally well [IOW when fed the right material they all seem to "disappear" leaving just the stereo image] to my ears but each has different requirements for listening room space and placement. the only ones that actually work in a small room, are the thiel and the maggie speakers. the vandy needs LOTS of space, no less than about a 300 sq/ft, in smaller rooms they get shouty at the crossover point [2.8kc] and totally lose their magical stereo imaging. i also have a mirage omnipolar and although i don’t guess they are time/phase-aligned, they image even better than the other 3 in my experience, again only if you give them plenty of space around them even though you can listen to them in the nearfield and get quite a spectacularly stable 3D stereo image that way with a wide sweet spot.

Room treatments do not add to coherency.  Room treatments subtract.  The speaker must produce a time or phase coherent sound field in order to produce that astonishing three dimensional soundstage.  The reflections- both airborne and the mechanical interaction between the speakers and the floor (as well as to the amps and other components) though small they may be smear the sound.  The room treatments remove those reflections to restore coherency and detail as well as bring more clarity to the bass.  That is my experience.  

No, these things don't on their own, make for a better speaker. It's not like this hasn't been studied for years. 

https://www.audioholics.com/room-acoustics/human-hearing-phase-distortion-audibility-part-2

^It might be imprudent to overgeneralize conclusions from this research. A loudspeaker that is phase coherent might not be time coherent, though a loudspeaker that is time coherent will be phase coherent. That there was some evidence reported (though deemed staticaly irrelevant)  of discernment of phase coherent recognition, then asks an unanswered question; were the correct responses consistently from consistent respondents?

From years on this forum, if there’s anything that I’ve learned, is that it would appear that while we all hear somewhat similarly,  many of us seem to listen differently. For what ever reasons whether consciously or subconsciously we often times prioritize different things when listening, and are more sensitive to different aspects of sound. I believe that some are more sensitive to time and phase coherence (perhaps at the expense of other attributes) than others. For those that are, I suspect that time coherence allows for a greater appreciation of transient detail, and a quicker neurological processing of soundstage and imaging cues as they are presented in real time.

A proper step response (in an appropriate space, at an appropriate distance) is perhaps the best indication of a time correct loudspeaker. John Dunlavy had said that once a a proper step response is achieved, everything else starts to fall in place. This suggests to me that time coherence could have advantages beyond the specific goal at hand.

Some have argued that time coherence only works for given listeners in specific locations. Adherents would argue that they work just as well as non- time coherent loudspeakers for listeners in less than ideal locations, but non- time coherent loudspeakers can never really work for any listeners at any locations.

In the past, making time coherent loudspeakers was a daunting project, that not many were capable of and/or were not deemed worth the effort. I suspect that as DSP and more integrated loudspeakers become more prevalent, so will time correct loudspeakers become more prevalent.

Every other component in the chain can maintain time cohernence without corruption, why not loudspeakers?