If there were no judges...
Everyone would feel like they deserve to be on stage.
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People judge, that's life.
It is better to give than to receive. You need to do things for people. Self-esteem, the ability to like yourself, only comes after you've done something that makes you likable.
You can't bs yourself. No matter what you tell yourself or what slogans you memorize about how everyone is special, you'll think of yourself as special when you do something special.
If you think you're special when you haven't done something special, you're not healthy and well-balanced; you're a narcissist, disconnected from reality. Amateur philosophers who try to instill "self esteem" in people are teaching them to disconnect from reality.
What you should do is teach the children to do something very well so they have no problem with being judged because they already know they are perfect.
Most judge on stage activities are basis.