This would parallel that the sharper a change in frequency response, the more noticeable it is at least in large systems. A change in DI would be modulating the spectrum of the off axis energy in the room.
I would add there is what i think of as the "source spatial identity issue" which is not easily measurable (as it is within the difference between two signals reaching ones ear / brain system that creates the 3D sound world we live in).
Imagine two different design speakers which have essentially the same Frequency response.
You walk into a room with either set playing and they both sound good.
In the stereo sweet spot, they sound entirely different so far as the image.
Ok first off, this could be the difference in sidewall reflections so you move outside on a quiet day and they still seem very different so far as stereo image even with no room reflections.
Now you listen to just one speaker at a time. With eyes closed, it is easy to point at the direction of both speakers BUT with one speaker, with your eyes closed you can easily guess how far away it is but the other is much harder, in fact with a soft muffled voice with reverb you guess it is much farther than a dry voice that sound up close. The difference is the ones that are still easy to hear usually radiate a complex radiation pattern that carries the clues your ears need to localize the source (my conclusion).
The pair that are easy to hear how far away they are, are the ones that stand out as part of the stereo image no matter what it was, they anchor the sound to that location in space, the ones that were hard to tell with your ears are the ones the disappear behind the stereo phantom image and can produce the most solid phantom image and your least aware of them as a source.
The problem with horns in most multi-way system is that if you have sources separated in space, your ears can also detect that as the source in time and space because there are small difference between the sources.
The more horns you have and or the larger they are (and true of direct radiators) the more spatial information those separate sources can carry in addition to the signal.
In other words once you are far enough away to not detect multiple sources, you still may well be able to localize the location in depth by the separate info reaching the right and left ears.
I would bet some reading this are skeptical about what i am saying about "hearing aspects of a loudspeakers radiation" and the effect on the stereo image part.
For those curious, I can point you to a simple DIY construction project which will I think cement what i am getting at.
First get 2 of these small full range drivers, i use these at work, they are pretty amazing.
https://faitalpro.com/en/products/LF_Loudspeakers/product_details/index.php?id=401000100
Make yourself a flat baffle about 2 feet square or maybe larger using 1/2 inch plywood, put a hole for the front mounting the driver in the center and cover it with 1/2 inch foam (use spray glue like super 77).
Then open the hole a bit and mount the driver through it and screw it down so it compresses the foam. You can add a small back box and go the T&S alignment if you wish.
This driver here radiates as a simple half space omni point source over much of it's range and can be eq'd until it complains and on axis goes up quite high but it is the very simple radiation over much of it's range and the wonderful stereo image these produce that is the point.
I have a friend that made these and he liked them so much they are his office speakers.
At work, the objective is this kind of simple fractional space single point source radiation but over smaller angles using CD horns
Best,
Tom Danley