Atkinson and others have hijacked "coherence" to include the smooth phase transitions in non-coincident systems with large phase shift - as long as the phase transitions are smooth, some call it phase coherentThat is certainly what I understand as one class of "phase coherence".
Thiel, Vandersteen and many physicists reserve the term "coherence" to mean that the phase response remains minimum, ie. it does not depart from flat.I look at some of Vandersteen designs and I am not sure how he could achieve that.
A good measure is "excess phase" approaching zero.Yes, in the strictest of the definition, that is true. But in reality, I am not sure if any speakers can meet that definition but I could be wrong since I have not seen all the designs out there. The latter Thiel speakers use coax drivers so maybe "time coherence" can be achieved without excess phase on the tweeter as it approaches 20KHz. In the case of Vandersteens, he uses conventional drivers with the tweeters offset from the midrange so I am not sure how he could do that without some amount of excess phase. So it's possible he could be sacrificing "smooth phase transition" at the expense of the tweeter excess phase?
I've seen John Atkinson measurement of the CS2.4 step response, and the peak on the step response does suggest that the tweeter response as it approaches 20KHz may not meet that "strictest of definition" as you pointed above. If a speaker meets the "strictest of definition" of "phase coincidence" , then the step response should be "smooth" on top of the step response where there lies the tweeter phase vs. the rest of the frequency (for example below the tweeter cross over point).
For example, if you take the phase at the cross-over point to be the reference, the tweeter phase will always deviate from that reference as it approaches 20KHz and therefore the speaker does not meet your claim of "phase coincidence" and therefore by definition, the tweeter response will not be "phase coincident" with the rest of the frequencies. And of course, some speakers are the worse offenders than others with this respect.