Why not horns?

I own horns as well. You should do a bit more reading before throwing around terms like "distortionless".

I dislike their sound.

if a room is lively already, horns might not be a good idea ( not saying it cant be done ), but maybe a speaker that is a little bit on the warm side would be a better choice.

The very best horn designs run at about 3% THD when played loud and this will distortion is audible and in treble.

Conventional non-horn designs can play loud at 0.3% THD and often much lower in the treble - pretty much inaudible.

You are talking at least a factor of 10 more distortion in a compression horn design...

The principle advantage of horns is that they are more efficient and play louder with less power. This efficieny comes at a price which is compression in the horn throat and a higher level of distortion at louder levels.

At modest levels horns can be very competitive in terms of sound quality/distortion.

I absolutely loathe horns!