I am not in any way saying that line arrays are perfect.
With the Line arrays I have had experience with (except for one) I have never experienced what you are referring to. The one that I really didn’t like was the EAW with the speakers on the sides of it, that one had the donut effect badly.
The one issue I did have was in one room because of how it had to be deployed and the shape of the room the sound hit the back wall and came back onto stage louder than I had heard from any other system. But the clarity and coverage was really good. And the slap back was livable.
I am going to again be on a d&b audiotechnik line array next Friday and I hopefully will have some time to walk around and listen for the behavior that you are describing. The first time I heard this install (outdoor venue) I was really impressed. And I am not easily impressed.
Here is a "kinda easy" way to experience it.
Take the line array and turn it 90*. So that it is wider than tall. You can do this with the "stick" lines as well.
YES, totally unusable, but this is for demo purposes.
Try to get it where the center of the boxes is somewhere around ear height. Sitting on road cases for example.
Do this outside-free of reflections (so they don't influence what you hear).
Now play music and walk from one end of the array to the other.
You should hear the buildup in the middle. ie the "donut".
If you have a tall mic stand, take some measurement "above" the array (which would normally be the side of the array)
Do this at the ends and the middle. You will see the build up in the middle-again the donut. This is where all of the energy is combining (think of it as power alley with subs).
