I used to band my feet when I ran barrels my horse had a big engine and I did not want to take the chance of losing a stirrup when I was moving him over or pushing around a barrel. It was two bands connected together in a figure 8 one over the toe, one over the heel. If I had fallen off the band would have broke.
I agree that children need to learn to keep their feet in the stirrups, and really if your not balanced or your foot is not positioned right one little rubber band is not going to help you. I have never banded my kids feet, but they are on steady eddy horses with small engines, there has been no need. Anyway kids need to learn how to pick up a lost stirrup, or ride without. But if your picking your leg up to push the horse over, or reaching back to hold the back end it gives just a little more hold.