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

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?

Past attempts at DSP were abysmal failures, but perhaps significant gains have been made in the past few years. Funny I still dont consider DSP a viable option which is probably not wise. Just dont like the idea of DSP at a fundamental level. 

@audition__audio , that is your own bias at play. It is just about numbers, ones and zeros. The very first step in the modern recording process is turning the music into those numbers. Once you are in numbers you can do just about anything without any added distortion. It is all about the programming which has improved over the past 30 years but the basics were well known 30 years ago. 20 years ago some very sophisticated processors were available but the mentality of us audiophiles shunned any added complexity. Our culture was used to the problems of analog devices and I think we generalized those problems to digital devices.

The improvements that can be made with digital processing far outweigh any downside. I digitize my phono stage to run it through a digital preamp/processor. You can go back and forth between the analog turntable and the 192/24 digitized one all day long and you can not hear the difference. The two major advatages of digital processing are being able to adjust frequency response, matching channels precisely and digital bass management with time and phase correction. IMHO you can not get to state of the art sound without them. Another way of looking at it would be, you can make any system sound better with digital processing. Also you can not get to state of the art sound by listening. You have to measure.

^The subject of DSP is perhaps for another thread. But, as pertains to the subject at hand; DSP can be make available time and phase coherence to those that wouldn't otherwise have the considerable chop's necessary to accomplish it, and make it much less time consuming to develop and considerably reduce the labor costs to implement it.