Every gym is NOT the same. Though I guess it depends on your area though. I feel extremely lucky that my daughter is at a gym with positive coaching. I have seen girls with fear issues on DDs L4/L5 team and coaches have dealt with it very well, no belittling, no cruelty. My DD has had vault issues/fears all season, but her coach has worked with her and been VERY positive the whole time. She has broken down at meets over vault, but coach was still positive. And even though Sophia may want to stay, she is only 7/8, not old enough to decide what is good for her mental/emotional health. I wouldn't be leaving practice either and I would pull her if she is put on vault by herself again, that is abusive and cruel.
And I am not meaning to sound like I wouldn't care about my child's feelings towards her teammates and gym, but I have a ZERO tolerance policy for coaches that treat kids cruelly. It is a huge issue to me and I get very sad when I hear stories like this. I can't imagine letting ANYONE, much less someone I am PAYING, to treat my kid this way. If a teacher did this, we would be outraged and pull our kids from the classroom, but I see parents let coaches do it all the time. I just do not understand it. Love of gym or not, my kid would do NO gym rather than be treated bad by a coach.
Good luck to Sophia at States. Tell her that her fears are very common. I think her vault is really nice and hope that she can find a coach that will work with her through her vault issues, not punish her for them.