Why not horns?

No, horns are THE OLDEST form of amplification. ;-) I'm not sure if they ever were all that popular in home audio. It can be argued that they were somewhat of a necessity before we had better amps. And the first electric amplification was with tubes so that technology, while ages younger than mechanical amplification, is considered outdated by many people today. But that is only their opinion. Both of these technologies do still work, and work well.

The average audiophile will not consider pro-audio anything because of a bias instilled by countless years of reading audio magazines. Horns seem to get lumped in with pro-audio, even though there are many horn designs that don't use pro drivers. No, I don't think the shift is due to outdated technology. There are quite a few designers today who use horns.

I think pro-audio got the balanced standard thing right. But they sure are ruining popluar music recording.

Unsound - Horns are the least exploited speaker technology out there. They are capable of lower distortion, greater dynamic contrast and quicker response. The combination of low mass and high output allows them to provide explosive sound and minute detail concurrently.
And does anybody think that horns are any more archaic than cones? The dome tweeter and conical midrange have been worked every way they can be and the last ounce of potential was wrung out of them long ago. Acoustic suspension is a parlor trick that can buy some compactness at the expense of speed, explosiveness and efficiency.
Horns are not yet well understood but the curtain is rising slowly and, I believe, we are nearing the threshold of a breakthrough in popularity which will create better and cheaper product. Maybe smaller too.

"why would "Horns have a greater potential than any other approach."?"

I'm in agreement with you on this question, Unsound. I gather from Microjack's most recent reply that he may be referring to the general masses, rather than what is already known by those who have studied horns for years.

Macrojack, horns have have historically had some of the biggest companies spending the most money trying to develop them. I don't see why you think they are capable of lower distortion. Yes, I think horns are more archaic. There's a reason there are so many more cones and domes, they make more sense. Even panels and omnis make more sense, at least to me. Speaker designers no longer need to compromise their products due to the limited availability of high powered amplifiers. Other speaker designs are capable of filling residential sound rooms with enough volume without the need for additional mechanical volume enhancers. Horns have been well understood for decades. Perhaps there might be advancements due to CAD, improved drivers and digital cross-overs, but those types of advancements will be probably bear more and sweeter fruit for other designs. Truth be told, many if not most of the advancements that might be available in horn development for home use, will probably never see the light of day, because they probably aren't worth the investment due to market considerations. What ever future horn development there might be, will probably be geared to commercial venue applications in which high fidelity might not be the highest priority.