As was said, "horn" only refers to the design of the speaker's cabinet - "horn" classifies the design just as vented, sealed, transmission line, etc. In fact, the horn design is the most efficient of the bunch, hands down. And you most certainly can have a bass horn - they just have to be extremely large (and heavy) to be functional at low frequencies, so they're somewhat impractical for a speaker cabinet that is going to be moved often. Unless you're a sound company with big trucks and lots of stage hands.
Why do bass cabinet manufacturers use horn tweeters?....................I think it's mostly because it's the cheapest way to add some sizzle. Sure, they're more efficient, but consider that most cabs with tweeters have an attenuator for the tweeter as well, and I've never heard of anyone who runs that thing wide open - they're just too harsh. And I think it's also a matter of "follow the leader". They do it, and so do they, and so do they, so we do it. A good soft dome tweeter is less efficient, but you can use two of them (as does Accugroove) to overcome this. It's not like they're terribly heavy or take up much cabinet space. And you will NEVER find any argument amongst audiophiles as to which sounds better - the soft dome is it.
The reason cabinet manufacturers use horn tweeters is cost.
