Not sure it’s a good idea. Why. My reasoning is the unfamiliarity of the other children. It can be threatening to a child under 10 to be placed with different children at different times. Whether you pay for it or it’s paid by government.
If you start a program like this how are local (PCP) doctors going to handle similar requirements.
This could be construed as a way to force veterans with young children to go to a Veterans Hospital.