Ha! Good for Jonathan! He's a first-rate ambassador for horns. He makes beautiful horns, and he helps make horns beautiful.
At first glance his little horn in that video clip looks a lot like the one we use in the
Gina speaker, which is also solid wood, BUT ours is not a "Conical". My understanding is that a Conical has a straight, constant-angle wall from the throat all the way out to where the mouth round-over starts. In my opinion the theoretical drawback is the virtually inevitable angular mis-match between the exit angle of the compression driver and the entry angle of the horn, which will cause diffraction.
Ours is an "Oblate Spheroid", which uses a specific constantly-changing-radius curve to make the transition from the exit angle of the compression driver to the coverage angle of the horn. The Oblate Spheroid shape was found by Earl Geddes to introduce the least amount of disturbance to the wavefront for a given amount of angular change, the intention being to minimize coloration. In other words, the Oblate Spheroid prioritizes transitioning from the exit angle of the compression to the horn's wider constant-coverage angle in the most benign way possible.
However IF the exit angle of the compression driver MATCHES the coverage angle of the horn, there would be no need for a transition, in which case I think a conical would be the ideal.
That little "phase plug" thingy is interesting. I'm not sure what its net effect would be, but I think it will break up reflection modes within the horn, which would be beneficial. He says that it helps with "dispersion", so it's apparently doing things that I can't yet wrap my head around.
My forthcoming bighorns will be Oblate Spheroids, so I think Jonathan will remain the ONLY one doing solid wood Conical horns.