Strange Klipsch thing

I owned KHorns for about a year and a half. I liked a lot of what they did and some things I didn't like. Image depth was pretty much non-existent. I unscrewed the top hats that house the mids/tweeters and angled them into the room and it helped a little but not much.

They are VERY dynamic, but have their faults as you state. The big corner horn K-horns playing Marche Slave about 50 years ago at a friend's house, made me an audiophile

A horn speaker placed in a corner will lack wall reflections that give a sense of depth. Horns are more directional than other kinds of drivers, so the only depth you will hear is that which is in the recording.
There are pros and cons to every aspect of speaker design. Room reflection is just another variable. It seems to me that I have heard a nice spread of image from k-horns before. It was a long time ago, but I was very impressed by them. I use Forte IIs, not in corners. They have a wide image and some depth, but not with precision of my Swans or PMCs, but the music does have a "live" feel. My Alons present in their own distinct way. Add the fact that different amps change the presentation...

"so the only depth you will hear is that which is in the recording."

If a system is manufacturing depth that is not in the recording then it must be an affect being created by the system which is no different than any other type of coloration.

With Klipschorns and a few other speakers like ESP and a model by NHT with a built-in toe angle it is important to be sitting at the proper distance from the speaker. If you are sitting at the proper distance the speakers should cross in front of you, about at your knees.

Your experience is the same as mine but on the other hand my Maggies fire half of their energy to the back wall. Is that re-creating image depth or just creating one? I like both presentations but some music sounds better on one speaker than the other and vice-versa.
Reflected sound is a personal preference. You have to decide how much reflected sound you like. If you don't like reflected sound, direct radiators will have the least amount of it.