Not specific to kids though. At best a mechanism to protect the over 50s, so in a school setting it would only be for the benefit of (some of) the teachers not the students.
That’s where a lot of the questions center: how much do we compel people (especially children) to do things that may not be in their individual interest, for the benefit of society in general. Covid vaccines for young children may well fall into that category, when you are weighing the low probability of serious illness against the (also low but possibly greater) probability of side effects.
The FDA has a truly difficult job balancing these considerations and it’s not made easier by pressure from politicians on either side.