I try to always remember that somebody everywhere knows somebody everywhere. You don't have to talk about, brag about, post or whatever. Parents text other parents, coaches text other coaches, kids take videos and pics and post them on social media before you know it. Sometimes innocently and sometimes to start trouble. I have flown across the country for job interviews in my other profession and met people that knew people/had relatives where I was working/living. I certainly never told anyone of my intentions but it got back just that quick that I was looking for a new position elsewhere. Which then strained things where I was, rightly or wrongly.
Is it right to ban an athlete? Definitely depends on the situation. Personally I have only banned one athlete in returning to a gym that I worked for. That was because they were openly and unashamedly trying to recruit the higher level kids to go to their gym to cheer. To the point she was pressuring the kids and slamming our gym's cheer program in the process. All while she was coming to our gym to tumble and stunt because we did that better than her cheer gym - according to her.
I would ban if it was a criminal act committed by the kid/parent. Especially if it was knowingly done. I also would potentially ban a kid if the parent was delinquent about paying their bill AND bragging about it/flaunting it to other parents.
If a kid moves on to follow their dream of cheering for a big name program, or they want to go to Worlds, etc. I wish them the best. I agree with
@Nikaa on that one, even though that recognition that it was a smaller gym that helped that athlete get to that point to be on the floor at Worlds and do so well was not always recognized by that athlete/parent or the new gym. But that is a different thread for another day.
Now I have worked for gym owners in the past that have banned athletes for trying out at other gyms, being friends with kids at other gyms, going to other gyms Open gym which IMO is totally wrong.