Nazis had the Hitler Youth. Communists had the Young Pioneers. Cults have their own youth groups. We have public school. The common denominator is that they, not parents, control what happens to children. They, not parents, decide what to teach, and what not to teach. They, not parents, decide whether first graders need Drag-Queen Story Hour and gender-confusion classes. They, not parents, decide whether to teach kids to salute the flag or despise it.
So let the CDC decide whether to require Covid shots (plural) for all kids from preschool to grade 12. It they go that far, for many it will be too far. Many states in the heartland will opt out of CDC control. And even in blue states, millions will pull their kids out of school and either home-school or establish their own schools. As any animal expert will tell you, the last thing you want to do is mess with the kids.