I’ve owned phase/time coherent speakers from Quad (ESL 63), Meadowlark, and Thiel (CS6, CS3.7 and CS2.7), and a lot of other designs using higher order crossovers.
I still have no idea if there is something audibly different and inherent to a first order crossover speaker, given all the variables involved. I can say that all the Thiels had a particular characteristic that set them apart from most speakers I’ve heard: a level of imaging focus and in particular, imaging "density" where, for lack of better explanation, it seems like all the sonic information related to an individual voice or instrument in the soundfield seems "lined up" right where it should be. No swimminess at all. It gives a real sense of solidity to the sound.
I have heard such characteristics imputed to time/phase coherent speakers, but then again the Meadowlarks didn’t have this quality to the degree the Thiels have, nor did the Quads (though I find all electrostatics suffer from a lack of palpability to begin with, so apples to oranges there).
I remember the first-order Dunlavy speakers having a similar density of imaging/tone/palpability like the Thiels as well.
Tonally I’ve heard many gorgeous 2nd or 3rd order crossover speakers. Paul Hales was fantastic in this regard and his Transcendance speakers were among the most tonally beautiful and accurate sounding I’ve heard.
But after a while I missed that sense of "thereness" and density I had from earlier Thiel speakers, and I eventually found my way back to Thiels.
Again, just some anecdotes, not really an explanation for them.
I still find all sorts of higher order speakers really fantastic, tonally, dynamically and otherwise.