There could be, IMHO, enough merit for a college/university to have a psychiatrist on-hand for consultation due to the inevitable first-breaks and drug use that happen on campuses.
When it comes to schools, I'm assuming you don't mean colleges. In that case the meds we prescribe aren't as effective and could be more dangerous. SSRIs, for example, in children have a higher risk of causing suicide. Their benefits are less in children compared to adults. Most of the interventions are psychosocial.
I'd rather have a child-psychiatrist chime in on this but the above are my thoughts. Child-psychiatrists often develop some knowledge of the local schools.