Bruce (Bifwynne), thanks for the summons. I haven't yet taken the time to read the links Bombaywalla was good enough to provide, but I am pretty much in agreement with all that has been said by the various posters above. Including the comment by Kiddman just above, which I believe to be a correct statement of the bottom line. And also including the comments by others to the effect that speaker technology is not one of my areas of expertise :-) And in that connection I'll say also that over the years I have found Tim's (Timlub's) posts concerning speakers to be highly knowledgeable, credible, and informative.
Another member whose inputs I suspect would be particularly valuable on these issues would be Duke (Audiokinesis); perhaps he'll spot this thread.
Regarding your basic questions about about how to gauge time and phase coherence, and about how important it may be among the innumerable tradeoffs that are involved in speaker design, I think that Unsound summed up the answers very well when he said:
Good step and square wave response are indications of wave form fidelity (time and phase). Again, as to it's importance, well that's up to debate, with opposing opinions prevalent on both sides.
Realize that a theoretically ideal square wave (which does not exist in the real world, of course), having infinitely fast transition times between its two states (i.e., risetimes and falltimes of zero), perfectly flat tops and bottoms, and no overshoot or ringing, consists of the summation of an infinite number of sine waves, one being at its "fundamental frequency" (the frequency with which its pulses repeat), plus others at every odd multiple of that frequency (i.e., the 3rd, 5th, 7th, etc. harmonics). The amplitude of each harmonic decreasing as its order (i.e., its frequency) increases.
In order for a real-world approximation of that square wave to be reproduced accurately by a speaker, at a given listening position, all of those harmonics (which collectively are generated by a combination of all of the drivers in a multi-way speaker) have to arrive at that listening position properly timed and phased relative to one another. No speaker will do that perfectly, of course, but results will vary widely among different designs.
In the measurements section of most of the speaker reviews which appear in Stereophile, John Atkinson presents and discusses the speaker's step response (which is pretty much as meaningful as the square wave response, a square wave consisting of a continuous series of positive-going and negative-going steps). For example,
Figure 9 here is the step response for the (very expensive) Vandersteen 7, measured at a certain height and distance. The step response shown is probably about as good as it gets. (Keep in mind, btw, that the step response of any speaker will not **look** like a step because, among other reasons, for it to do so would require that the speaker's frequency response extend down to close to zero Hz).
So perhaps some degree of insight into the importance of time and phase coherence could be gained by comparing that measurement for speakers whose sonics one is familiar with and that have been reviewed by Stereophile, and trying to judge the degree of correlation that exists between the quality of that measurement and one's subjective preferences among those speakers. Although to be meaningful, that would have to be done by a given listener for a considerable number of speakers.
I've never done that, btw, and unfortunately I don't think that such measurements are available for most of the speakers I've owned or extensively heard over the years.
Best regards,
-- Al