Horn based loudspeakers why the controversy?

… Most horn systems are physically large, and like a lot of other large speakers, they deliver a "big" sound. The sound seems to fill up a large volume of space and envelop the listener. I like this quality a lot. When one listens to tiny speakers, even when they play quite loudly, one can sense that the sound is coming from a small source and it does not seem to have realistic scale.

I wholeheartedly agree with the above. Being ’enveloped’ (a very fitting term here) by sound the way large horns can do while providing proper-ish scale is what really sets them apart from most others speakers, I find. Another aspect that is inherently linked to this sensation is that of effortlessness; it de-stresses the sound in a way that is both relaxing and more believable. Smaller, direct radiating speakers can sound "large" in a different, spatial way, but they don’t load the listening space in the same authoritative, solid and room-lock kind of way.

I'll agree with most of the above, and most of that is exactly why I dislike horns. I've never attended an acoustic performance that sounded anything like what I've heard through a horn system. A quartet doesn't sound room filling or enveloping. It doesn't have startling dynamics. It doesn't sound huge. The scale and imaging I find in the live performances I've heard is much more like the dynamic speakers I've heard than any horn. 
I'm sure I'll be jumped on because I've never experienced a live acoustic performance that's sounded anything like what horns do. I've never heard any violin, clarinet, or kettle drum really sound huge or enveloping in any venue. 

The most realistic sonic presentation of an orchestral piece I’ve ever heard came from a really good movie theatre system employing horns.  Eyes closed it was astonishingly like listening to a full orchestra!

Non sound reinforced (i.e. simply acoustic) shows are far different from otherwise, and an acoustic quartet certainly does have "startling dynamics" to the musicians playing the instruments, and maybe anybody within 10 feet of them...but that's about it. In my sideline as a working soundman I've mixed hundreds of acoustic shows that DO have a clean system to run through...from the Baltimore Consort to John Renbourn to various jazz artists, and I love actually hearing those otherwise lost dynamics...through horn loaded systems of course (or phased arrays which also work). From a single large diaphragm condenser mic (classicial trios and bluegrass ensembles mostly), to multi miked whatever, the passion and dynamics of well played music is better when people can hear it, and well made generally horn loaded speakers make that possible.