I think something like this could be interesting and helpful.
I'm a psychiatry resident, and recently I've actually been talking to some people about how I think this job gives one a much more nuanced view of the police.
There are times that I do, honestly, worry about some of our very ill patients getting into trouble and being shot by the police. On the other hand, I also recognize that if someone's brandishing a weapon or something, it is going to be difficult to discern quickly whether they're ill or just a criminal when it's dark and you're just approaching the scene in a cruiser.
So many of our patients are helped tremendously by the police. Somebody found these people doing all sorts of concerning, dangerous and even threatening things but had the good sense to bring them to get treatment rather than bring them to jail. Some of these people will cause injury to our staff even in the controlled setting of the emergency room, so it takes a lot of character to deal with them compassionately in an environment as poorly controlled as the streets.
On the other side of it, occasionally somebody will fly under our radar and we'll admit somebody to the hospital who is just a straight-up criminal. When there's really no illness to treat psychiatrically, the person has multiple warrants for crimes of targeted violence/weapons/etc., and they've been making clearly understandable, motivated and specific threats, all you want is a police officer to come and handle the situation.
The police really do work hard to serve the best interest of our patients while protecting hospital staff and the rest of society.
The one thing I do wish the police in my area would do better is respect our policy of not carrying their firearms onto our psych units as a matter of course. I'm generally quite comfortable with firearms and personally believe strongly in the second amendment. That being said, we search everybody on our locked units and it is certainly not the streets in terms of the risk of the patients having weapons. There have been some disastrous outcomes of police carrying their firearms onto the unit/psych ED in the past so we request that they not enter the units armed. They always seem to come armed no matter what.