Well I haven’t read all the responses here, just some of them. I have not had a stall kicker of my own, but have known several that I did not own. One was “cured” (or stopped) successfully with kicking chains. It terrified me, but it worked.
The other was a horse that belonged to my vet, and was boarding at our farm. A “fancy” show hunter. Kicked the chit outta the walls of the stall at will, at feed time, anytime for any reason, and the stall was open 24/7 to the paddock. Fortunately, our stall walls were very strong, indestructable. But it was pretty scary to watch. The horse was moved to another boarding situation, box stalls without a paddock attached, which I felt was gonna be interesting. The stall walls were made of poured cement. He kicked that stall wall only once. Never again. Problem solved, I guess.
So there’s a couple of possibilities for you.
I think that some horses like to “make noise”… it gets attention. Any attention is good attention… the human comes over, waving arms and squeaking. This is “success” for this sort of horse. Same for a horse who hammers on his stall door with pawing. They like the noise, it “works”. One of my most favoured equines did this. He ran the barn, directed humans to do his bidding… whack, whack, whack on the door- “Hop to it, human!!!”. His stall was open to his paddock 24/7 always. I opened his stall door, and tied it open 24/7 with a stall chain across the doorway to keep him in, and put a rubber mat outside the door, in the aisle, so it made no noise to paw and he had nothing to whack. The behaviour stopped, because it didn’t work for him any more. He was always fed first anyway. He was smarter than most people I meet. And devious and inventive.