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

One on a very long list of things that make a better loudspeaker. The ones I have now are light years better than the previous ones, even though they were beautifully and conspicuously time-aligned and the better ones equally obviously are not.

some people are essentially deaf to it. Move on if it doesn't float your boat. My favorite Strad player " gets it ". So do I.

Absolute phase gets thrown out the window with multi-track pop/rock recordings. 

Not being time and phase correct does not eliminate a speaker for me. A time and phase correct speaker has a "rightness", for lack of a better term, that a speaker that is not time and phase correct does not have IME. The negative that I have seen with them is that many of them will suffer dynamic compression when pushed hard. It is a trade off and depends on listening habits and what one truly values. As stated above, some either don't hear it or don't place that much value in that particular trait. To each their own.