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.

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?"

Y’all get the crappy lossy cabinet output shows up in the impulse response, and more importantly the waterfall...right ? All easy to hear.

Mijo in 1983 I was using an FFT program on a Commadore PET in the design of loudspeakers.... I feel like Lew... hackles and all

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

One cannot change that too much with DSP. 

With my DSP controlled active speakers I can set them to linear phase or low latency the former is delayed 30ms to align the drivers the later turns off linear phase for a 3ms delay. I can't tell a difference but my room isn't an anechoic chamber.