UPDATED with input from Goldie.
The United States Olympic Committee (USOC) is the National Olympic Committee for the United States. It’s based out of Colorado Springs.
USOC is the organization recognized by the the International Olympic Committee.
Similarly, USA Gymnastics ( USAG) answers to the USOC.
USOC could decertify USA Gymnastics and indeed they made that threat. As a result the entire board resigned on January 26, 2018
All those organizations are natural monopolies , not much subject to market forces.
You can quit USAG and go to the United States Association of Independent Gymnastics Clubs, but getting to the NCAA will be more difficult. Olympic qualification impossible.
If interested in this topic read a WSJ article by Steven Sexton. Subscription may be needed.
The U.S. Olympic Monopoly Needs Accountability
There can be only one Team USA, so Congress must provide oversight and force changes.
Gymnastics Coaching.com 