If the coach is not concerned about your young child's back when they are doing bridges at the age of 4, I question if they will be thinking of your child's open growth plates when they want them to start working even harder skills - like Yurchenkos on vault, 1-handed BHS on beam, to name of few as a pre-teen going through puberty. I feel you have a right to ask question coaches actions when the safety of your child is at hand. A bridge at the age of 4 is not going to have any impact on her gymnastics, just like a 1-handed BHS has not had any impact on my child's ability to do a level 10 beam routine! It's your choice, it's your child.