I have a lot of feelings about this whole situation, but I'll throw in my two cents from a high school coaching perspective. I definitely think USASF should have something similar (obviously it wouldn't work exactly the same since school cheer is a whole different ball game).
Here in AZ, if an athlete switches schools during the school year (regardless of sport), they can only compete in 50% of AIA events at the new school unless they appeal it directly to the AIA (our high school sports governing board). The only situation AIA will release the athlete fully for are if the parents moved for a legitimate reason (a big one at my current school is that it's near the Power Plant that is currently hiring, so people are moving out for their jobs), or if there is documented signs of abuse and/or bullying (I've never heard of this one actually being utilized). That's pretty much it. I've seen so many kids try and appeal and pretty much every time they get turned down.
The thing I like most is that this means that the schools and coaches themselves have zero say, and the athletes don't get to try and bring emotions into it or manipulate situations. It all boils down to facts. Again, I get that all star is WAY different since people don't attend gyms in their zip codes and they're paying customers. But if something like this was implemented then the coaches wouldn't be to blame if they kept an athlete, but they also couldn't have sole control over the athlete being forced to stay. It would literally just boil down to "hey can you prove that you had a legitimate reason to switch other than I don't like my spot in a routine?"
Again, I get that these people are paying customers, and that complicates things a bit. But I do believe this is an important rule, and even though it's not perfect, it does have a purpose for being put in place. Also, in a much smaller role, my brother did Pop Warner football as a kid and you weren't allowed to switch teams during the season, you either finished it out with the team you joined or you quit all together until next year. So it's not an uncommon rule for kids' activities (yes, even ones you pay for) to have.