Horns: Why don't they image well?

Partly correct, but for many years horn systems have included "phase plugs" or their equivalent to keep horns from "beaming" high frequencies.

This statement is problematic. Phase plugs are used to prevent cancellation at higher frequencies, thus extending the upper range of the device.

@kosst_amojan
Horns have to get pretty enormous to really play bass.

My speakers play a compromise on that- they use TAD 1602s (15", free air resonance at 22Hz, 97 db 1 watt 1 meter). They are set up with two woofers per cabinet. No problem playing flat to 20Hz. But the rest of the system is horn based. I've often wondered what a system like this could sound like if a Lowther or the like was employed using the same 500Hz crossover frequency.  But it images great (which doesn't come from a woofer anyway) so its been more of a thought exercise than anything else.

I don't find that the older horns imaged as well. As horn designs improved with the advent of CAD, so did the imaging.

But a lot has to do with what you hook up to them- and those older horn systems were designed for amps with higher output impedances. If you hook up an amp with lower output impedances, the crossovers often don't work right. I've no doubt that would affect their performance!

Horns tend to give a wall of sound, but rarely can image pinpoint in the horizontal and vertical and depth like the above ones mentioned can.

This statement is simply false.

It may be true for some earlier horns as the throat design and curvature of the horn flare affect its response. These days that is optimized with CAD; horns can image as well as any other tech.

Duke has made some great comments addressing the topic, answering it to its fullest.
If you don't get the nerdy part of it, it translates as:
"A well designed horn images as well as any other speaker".
Having made a good number of my own recordings, I can attest to that fact, by using those same recordings. Its not just theory- horns have been some of the most musical and involving speakers I've heard (Duke's amongst them, and his are unusually good deals on top of that), including their ability to image and play depth.