You need police in hospitals to maintain security for the patients in there. It's not uncommon to have incidents with people from the outside trying to assault/murder someone they know in the hospital. Criminals shot on the street still have to go to the hospital and this leaves an opportunity for their would-be-murderer to come in and finish the job.

Schools, it's sad but I'm in favor of school resource officers. Those people were good to have around and can serve as a role model.