To the OP, part of the problem is some parents actually want abusive coaching. They think it will make their kid a champion and they want that more than they want a healthy child. This empowers coaches who are abusive.
Example: I once inherited a fear-filled L7. although I barely had a chance to work with her daughter, her progress with me was not "fast enough" for her mom. At parent conference #1, I suggested her daughter work with a local sports psychologist who had successfully worked with our team. Her answer was, "if gymnastics is a sport where you need a psychologist, we'll find another sport." At parent conference #2 (2 months later) I went over everything we had tried in the gym to get her daughter over her fear and the small progress her daughter had been making in the past 2 months. It wasn't enough for mom, so I asked what exactly she was asking me to do. She leaned into me and said, "I want you to scream at her until she does what you ask her to do." I told her I was not that kind of a coach, because my goal is to create internal motivation -- not to motivate through fear. I told her that method would only work long-term if I kept getting scarier and scarier as time goes on. I then told her a few horror stories about a gym 20 minutes away who was very big on screaming, shaming and belittling. She packed up her daughter's locker and joined that gym the very next Monday. She also recruited 2 other GCMs to follow along so that their kids could be screamed at. Her daughter repeated L7 (did okay), went onto L8 (not as successful as L7), tried to compete L9, but scratched the entire season due to mental blocks. The next time I ran into the mom, ironically it was in the waiting room of the sports psychologist I had previously recommended (she was conducting a weekend workshop for local gymnasts). The kid was miserable and finally quit a few months later. The other 2 who followed also quit by age 12 due to burnout.
Another example: I overheard 2 parents from another team (the screaming, shaming and belittling team) discussing their daughter's fears. Mom #1 states that she feels so bad for her daughter because she has been going through so many fears. Mom#2 starts preaching to her that she needs to tell her daughter the same thing she tells her own, "You are not allowed to fear a new skill. Your coaches wouldn't have asked you to do the skill if they didn't know you were ready. If I hear about you balking over a skill you are told to do, I'll consider that being disrespectful to your coach and you will be grounded."
Another factor is most of us coaches are former gymnasts. Many of us had abusive coaches. A few decades ago, most gyms had no windows in their lobbies and team travel consisted of parents dropping us off at the team van which was driven by our coach to the travel meet. When you've come from an abusive environment you react one of 3 ways: get out of the sport and stay out (do not allow your own kids anywhere near it); stay in the sport and make up for your own abuse by nurturing the kids you coach; or becoming an abusive coach. Since there are enough parents who approve of abusive coaches and enough coaches who choose abusive methods, you have a match made in hell for the unfortunate kids in their care.