What if in many areas, the police received medical training and responded on all medical calls. One of the towns we cover, all the PD has medical training and they respond on all medical calls. The citizens know this, and expect the cops on every 911 call. This has several advantages.
First, the non compliant patient will not get all mad and ask why we called the cops on them. I have had potentially hostile patients become extremely hostile when the cops walked through the door. However, in this town the patient expects it. (It has also cut down on BS calls from what I am told.) Family members also can get hostile when the cops show up. Especially since many of our "customers" as well as their families engage in activities that are slightly less than legal.
It cuts down on response times. While we have excellent response times in this town, the cops are still on scene before us almost all of the time. They mitigate many potentially violent situations before we even get on scene. Also, because of their EMT training and AEDs in the patrol cars, this works out well in cardiac arrests.
It also helps immensely with crowd control. People tend to back up when told to by a cop rather than a paramedic or firefighter. Some people may disagree, but in my opinion, one or two police officers often do a better job of scene and crowd control than a 4 person engine company.
The cops in this town have greater community support. Even if all they do is first respond and put grandma on O2 before the ambulance arrives, at least they did something positive in the communities eyes rather than just write tickets.
Another thing my company does that I like is program the police frequencies into all our radios. That way, when we respond to a call PD is responding to, we can monitor the frequency and get an idea of whats going on before we get there. Some nights, when all hell is breaking loose, we monitor the PD frequency to get an idea of whats going on in the cities and towns we cover. It's amazing the number of times someone gets injured in a fight and the RP calls it in as an unknown medical or asthma attack because they don't want the cops coming. More than once, our crews have been responding to a address and heard a call on PD go out for a fight at the same address called in by a neighbor or passer by. Situational awareness can go a long way in preventing potentially violent incidents.