Horn based loudspeakers why the controversy?

@atmasphere 
Yes. There is the theory and there is the practice. I would also agree with your assessment of distortion and dynamics. I've long said that truly high fidelity allows for listening at very high volume without a sense of real loudness and what you say squares with that. 

The best system I’ve heard Austin Acoustic system they are using Horns....made by Austin Acoustic as well... Dynamic is out of this world? $750k, they were in Chicago Axpona 2017

For the record the quality of the compression driver makes all
The difference in the world . Here us a great example 
Pure Audio Project  open baffle  Horn  model. All these speakers are modular  ,they share 4- 15 inch Emenence drivers, 
There us the Horn , Voxativ full range for mids- highs,Tang Band,
Beyma150,AMT - Heil ,AMT-, you have full control ,as well as the Xover. A interesting take at something different,and you
Put it together.

I owned a pair of A7s from the early 70s until the mid 80s generally doing bi-amped live sound duty, and when used as stereo speakers from time to time they were astonishingly good. Not "flat" by definition but they had a charming, perhaps faux, "wooden" tone that was cool…this was before phase plugs and other refinements (although I replaced blown horn diaphragms here and there and added serious JBL 15" bass speakers to them) so it's a wonder they worked at all, but man, you could make people smile playing dynamic orchestral stuff through them, which I did occasionally by driving them with my home stereo rig…cool speakers.

I believe any and all Altec compression drivers had phase plugs. They changed some of their characteristics  (Tangerine) to extend and smooth out high frequencies.
Cheers, 
Tim