sometimes you can even hear the horn honk coloration on voices...I know some horns don't have this..You are right- some horns don't have that at all. It all depends on how well the throat of the horn is designed; many don't have the benefit of computer optimization but some, like the Classic Audio Loudspeakers, do. This makes them very free of any 'traditional horn' artifacts. The Kapton surrounds help as well, since the driver won't break up if driven at too low a frequency. Often you can't get away with a 6 db slope on a compression driver, but the Kapton surround allows for exactly that.
Take a look at some of the AV Showrooms videos on YT. Peter never seems to have any complaints about the Classic Audio Loudspeakers.