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

The human ear brain processing can differentiate between the initial primary sound and the reflected sounds so long as there is enough time between those sounds. Something that microphones are challenged to do. Which is not to say that microphones and the measurements they gather are not important. Just the opposite. The vast majority of manufacturers of time coherent loudspeakers recommend pulling their loudspeakers out from nearby walls for this very reason. Those time coherent loudspeakers that are meant to be placed in, on or near the wall are designed with an understanding of the unique predictability of the affects of this proximity that would not otherwise be available with all the differing variables of users placement and variables of users rooms, and  compensation is built in accordingly.

@jjss49 , flat is always the best place to start.

not debating that point (starting point, reference point) - my statement refers to aiming for a perfectly flat measured speaker response as a sonic end point

The human ear brain processing can differentiate between the initial primary sound and the reflected sounds so long as there is enough time between those sounds. Something that microphones are challenged to do.

So true. I once challenged a dipole mic, which sound came first? Said it could go either way. The condenser mic would only say, "No." The omni of course gave a much longer answer, "Yes." Tried a tube mic, pretended at first not to hear me then started glowing red hot. So I gave up, and haven't challenged one since.

A wise old uncle once told me,  "If you can't dazzle "em with brilliance, baffle  'em wth bulls__t."

...my statement refers to aiming for a perfectly flat measured speaker response as a sonic end point

But the thread is about the time domain performance of a speaker.

One cannot change that too much with DSP. The impulse response can be cleaned up somewhat. But in the edges of the crossover bands it is not really possible to do much in a passive system compared to an active one.

Once the non-time/phase aligned system and the time/phase align systems are in place, then either/both can have the frequency response dialed into what ever is asked for.

And the question then that the OP sort of asked is, "will they sound different?"