Why not horns?

Duke, as I have said before, it would appear to me that some people seem to be more sensitive to wave form integrity than others. Of course those people who might not be as sensitive to wave form integrity, might be more sensitive to other aspects of sound reproduction. Though I don't have any hard statistical research to support this, the market seems to bear it out. There are many successful speaker manufactures that don't prioritize wave form integrity, and very few that do. The few that do, seem to garner consistent positive reviews, a loyal following, and enough sales to make them most successful in this highly competitive industry.

I use my horns in a two way application with a light, fast 15 inch Italian woofer. The crossover is set at 400 Hz. right now with 24 db LR slopes in both directions. I cut the woofer off at 33 Hz. and let the horn reach for the stars. My compression driver has heat sinks and is designed to play up to about 40 db louder than what I use it for.
I have a conical wooden horn made of solid cherry wood that does not seem to color anything. I'm not sure about the validity of these few comments about disadvantages in horn use but none of it seems to apply to my set up. I've listened carefully over the last few days fo signs of coloration, phase problems, compression, etc. and no symptoms are apparent to me.
Bill Woods, who designed my horns and sold them to me along with aluminum throat adaptor and B&C driver, says that these represent the best midrange he can provide and that he has tested and measured them against QUAD, Manger and Heil, which he says are the best other mid range producers. To be honest, I don't remember if he also mentioned Walsh. We haven't talked in a while.
In any case, I am not a technician and I am not one who believes I possess superior listening skills. What I can say is that I am unable to hear any lag between my woofer and my horn, and that is a tone and body to musical instruments (timbre, I guess) which I never heard equaled by any other speaker.
Perhaps I'm the one who is guilty of lumping everything together. I don't get out much and I haven't heard any other horns in years. Maybe mine are not so representative of the breed as I assumed. Nonetheless, my horns do represent what is possible and I think that a larger company could produce this caliber of work at or below Bill's prices if they could justify the research and tooling. Bill has probably already provided much of the former and the latter can be outsourced reasonably, perhaps even domestically.

Duke I agree. That to large a midhorn to low a crossover point can cause problems. Why I'm now using a oval tractrix horn this allows proper integration of drivers the oval tractrix horns has solved a few problem of round tractrix maybe give one a listen not to costly. I crossover tweeter to midhorn about 6khz midhorn to midbass about 1khz. This way I can physically time align drivers in vertical array. I also design horns so tweeter midrange can be adjust in angle so you can converge at very close listening distances if you want. Its a pain to design this way everything gets large fast. Cabinets get complicated. Crossover parts horn comps etc all need to be matched with much thought. But end results more than worth the effort.

Unsound, what do you mean by 'waveform integrity'? Is this in the circuit of the speaker or is this the output, etc and how does this relate to phase angle, if it does?

I'm pretty sure that Duke is trying to get the best fidelity out of his speakers and I have not seen that phrase used before, so I want to be clear about what you mean by it. TIA

Atmasphere, time and phase coherence, or as Duke refers to: "waveform fidelity".