While I am just now beginning to train younger athletes, I thought a coaches perspective might help... though I must point out - I am but one coach, with my own opinion that others MAY share.
I think injuries to young gymnasts (and older ones) come down to education - of coaches, gymnasts, and parents.
For a coach, knowing the fundamentals of the skills is never enough. We spend hours with our gymnasts, and it is our responsibility to know our gymnasts level of mental and physical growth. Is this totally feasable? Probably not - but with our experiences, we begin to see patterns in body types, aggressiveness, and confidence. I know I have learned so much in my short time of coaching about personality and training that I know what mistakes not to allow again.
However, it is also a gymnast's responsibility to know their own limits, and do what they find necessary to move past those limits. The whole process of development from younger age groups to optionals is about progression. As we know from students in schools, not all students learn the same thing from the same activity. They may get a peice of the puzzle, but only a handfull will get the whole picture - concepts need reinforcement, and alternate teaching methods. When a gymnast truly loves to be in the gym, they will go to open gyms and "play." It is here where most of the "learning" is accomplished - even if they are working on front flips as a class, feeling confident enough, spacially aware enough, and driven to accomplish the skill, is what will help keep them safe. The only way to do that is through experience, trial and error, and (sadly) a few knocks and bruises.
Parents, hopefully, will understand the concepts of progression as well, and know their children well enough not to put un-needed stressors on their children. We all want our kids to be safe, and we all want to make sure our kids are having fun. It is never a question of letting a child "make a choice" for us, but helping and guiding our children towards making the right choices for themselves. If there is ever a doubt about a skill or training in a gym, it is every parents right and responsibility to talk to a coach about it. If the answer is not satisfactory, the answer is not to yank the kid out of the gym - if the kid will miss the gym, do you think that is right? Why take away something that they love? The answer is making a choice that will help your child find happiness and safety - you can either request they do not work on the skill (as said above), or wait until they are ready, and if that does not work, or you cannot find a happy medium, there is always another gym.
There is a chance in any sport to have injury. It is the nature of the act of doing. You can be sleeping in bed and get just as badly hurt as in a gym. Sure, there is far more potential, but it is possible. The questions comes down to luck, preparation, and security.
I have, in a high school setting, been exposed to injuries from track (knee/ankle/heel/toe), football (acl/knees/ankeles/shoulders/kneck), wrestling (almost the same as football)... so many sports... even golf! Knee and back issues abound!! Sports are very essential for youths - it gives them a sense of belonging, a sense of purpose, and a place to alleviate frustration and learn life lessons. It is a social builder, a component to trouble shooting, and above all - it keeps them more healthy than sitting at home and doing nothing.
The only reason I would ever take a child out of a sport (gymnastics or otherwise) is if they do not like it. Not because it is hard, not because they aren't "getting it." But because they simply have no desire to be there. To me, that is how they are going to get hurt. When they stop caring, it's time to move on to something else that keeps them active and enjoying themselves. Gymnastics is not for everyone - but the exposure to it helps in so many ways. Learning to fall, learning to understand yourself and your surroundings and how you interact with your environment, and learning how to work through some of the hard parts of life, where you feel like giving up and need that extra push to keep going...
There is a difference between being hurt and being injured. Please don't confuse the two. If you havent noticed - I love coaching, and I really love gymnastics. I have taken my beatings to make sure my gymnasts are safe - but not all coaches are as big as I am, nor willing to take hit as I am. However, there are others like me, who are willing to do what it takes in their power to save a kid from getting hurt, and spend the time to learn to train them properly. We are out there, and Im sure there are many of us, and many of us on this forum.
Best wishes,
Ryan