And the schools are not closed right now because of the fear that younger children are going to get the virus. Schools are closed because teachers are (rightly) concerned about getting the virus, and families are (rightly) concerned that their children might pick up the virus at school and bring it home with them and infect more at-risk individuals. If the teachers and family members are vaccinated, then I think it is pretty clear the risk/benefit analysis would highly suggest sending children back to school, even if they aren't vaccinated yet.
Schools in the US have already opened in many places before there is a vaccine, so I don't doubt schools are going to be opening ASAP, and that is almost certainly before most children are vaccinated.