In fairness, most people that like horns with collapsing DI usually like other features about them. It isn't the lack of CD they like, it's the acoustic EQ they get. Or some may like them just to fit in with a particular orthodoxy.

But the fact still remains. Constant directivity is a requirement of balanced sound. If the sound source doesn't have constant directivity, then off-axis sound is unbalanced. That also means the tonal balance of sound reflected back from the room is unbalanced. You can treat the room, but you're still just masking the problem.