I've owned coax speakers (Thiel) and listened to a number of others - e.g KEF, Tannoy, more recently the SourcePoint 10s.
I have not found any particular advantage just due to a speaker using a coax design. I don't for instance find the KEF, Tannoys or SP10s "extra coherent" or casting a soundstage unlike I can find elsewhere. In fact I've found a number of speakers, even the old Shun Mook Bella Voce (Shun Mook!!!) speakers to strike me as more coherent than for instance the Tannoys or SP10s or even the KEFs.
That said...I have found the two most recent Thiel speakers I've owned - Jim's last flagship 3.7 and also the 2.7s - to be just about the most coherent multi-driver speakers I've ever heard. Especially the 3.7.
I had the Thiel CS6 at my place years ago which had their then-new coax midrange/tweeter. That speaker sounded very coherent with the exception of a slight change in character with listener position, especially vertically a bit as I remember. I think some form of interference was producing a slight "hollow" sound from certain positions.
It seems that Thiel finally nailed the coax design with his last version - the tweeter set in the "flat" (corrugated) midrange driver. That speaker's midrange and treble (and bass) was just totally coherent in my home. Same with the 2.7. I can not for the life of me "hear out" the difference in drivers, any transition, cancellation or anything. And it maintains it's character over a very wide area. The sound is very consistent even when I stand up and walk around the room.
The other thing with the Thiels is the insane imaging prowess. There is a focus and precision and density to the imaging I have rarely heard before. Even my Joseph Speakers, renowned for imaging, sound slightly diffuse and less tight when directly compared with the Thiels.
So ultimately I have no idea how much of this to attribute to the fact it's a coax driver for the mids/highs, or to the first order/phase coherent design, or to any number of other design choices in the Thiels.