One other thought, in the coaches' defense, a lot of times they deal with parents who believe their child can do no wrong. In those cases, even something as simple as asking the child to sit out for being disruptive would cause ire from the parents. "How dare you sit my child out! I'm PAYING you to train her!" I'm sure you all know the type... so really, what's a coach to do? Obviously, as I said before, yelling and the like are never acceptable but some parents leave the coaches will few alternatives.
You are right about that, but in that case, they can always leave and find another gym. Coaches do have a tough job, but as you said, yelling, belittling, etc have NO place in the gym (or anywhere for that matter).