Why not run police to medical calls? They would get there before fire or EMS.
It will make more sense to send police than fire they will get on seen before fire or EMS. Unless you need manpower.
Because most police aren't EMT's. Firefighters usually are. Most departments around here will not hire you unless you have or will get your EMT. Most departments require FF1&2 and EMT-B.
And why would you think the police can get there before fire or ems?