Some of my findings actually shows that intentionally making time-phase may result in inferior phase problem and NOT betterI think that was also what I said in my original post. What I said that everything else being equal, then yes, time-phase coherent is a plus. But I also said that I have seen examples in which the designers tried to make time-phase coherent at the expenses of other parameters such as phase-mismatch or frequency response that may end up creating more problem than it solves.
It seems that Thiel (an I am being VERY careful not to appear to make any false accusation) has claimed that the company's speakers have very small excess phase, which means that the phase shift of the entire frequency range (from 50Hz - 20KHz) has very minimal phase shift, and based from Tom, within a few degrees. Now that is EXTREMELY difficult (trust me) and I do not even think it's doable or even REAL. I tried to model one of my speakers like that and I could only achieve about +/- 25 degree but I had to bend over backward to get that done at the expense of freq. response and proper driver integration. Therefore I really did not like the design and I think I am better off with a more conventional approach. But having said that, there may be about 2 or 3 speakers in the world that can have +/25 degree excess phase. John Atkinson had said that you can count will all the fingers in your hands the number of speakers he measured that can get a proper step response which is pretty hard in itself. But having a proper step response AND having 0 excess phase is like winning the lottery every single week.
For reference, if you use 4th order (24db/octave), you automatically get an excess phase of at least 360 degree. If you do a regular 1st order but with one of the driver inverted, you probably get about 180 degree of excess phase. To have zero excess phase (or close to zero as claimed by some) is like hitting a bull's eyes from 7Km away. I think you can count with five fingers the number of speakers in the history that can achieve 0 excess phase.
When you look at the step response from John Atkinson measurements, it's easy to spot if a speaker has too much excess phase. Even if a speaker can achieve a proper step response, if the initial spike is too "spikey" vs. the rest, then it probably has too much excess phase. I've seen various measurements of Vandersteens from Stereophile, I doubt they are qualified as "time-phase coherent" across the entire freq. spectrum. Maybe from 50Hz to up about 7Khz but not all the way to 20KHz. And I also posted the CS3.7 measurement and showed it to Tom and I said I doubt about the claim as well.
I have quite a few real world data and simulations but I am waiting for better Confirmation before posting the data since I don't want to be accused of not have REAL or FAKE data. I've heard of a lot of people including all the experts in the world talking about it but at the end you get even more confused! Maybe it's a secret and once you know it, you don't want to share.