There are very few horn loudspeakers that are not hopelessly colored. Classic Audio speakers are the best I have heard. Making thin walled horns out of wood is plain asking for it. A loudspeaker is not supposed to be a musical instrument. It should be only a transducer, nothing else.
The only serious advantage horn speakers have is efficiency. While it is easier to make them dynamic they do not own the store in that regards.
I have not yet heard a horn system rise to the level of the absolute sound but I do not see a reason why they should not be able to get there. The settings I have heard them in have not been well controlled. With dynamic speakers it is usually the crossover and lack of directionality or uniform directionality that keep them from rising to the ultimate levels. (can't wait to hear my buddy's new Magico S7s) Horns are very directional which is a good thing, Classic Audio speakers uniformly so. It comes down to the crossover and it is not easy to design a really good one. The problem is essentially the same for any multiway system. This may be the magic behind full range speakers. It may be easier to get them to image properly and the people that love them hold this more dear than reproduction of the frequency extremes? Just a guess as I have never listen to or played with a full range speaker/driver.