In most urban areas, PD stands there and looks pretty, gets photographed in the news, rushes in past you and holds a flashlight on what's going on, or gets info so they can write a report.
I actually subscribe to the belief that if it's on fire send a fire engine, if they are sick or injured send an ambulance, and if a crime was committed or if its an unsafe scene, send law enforcement. No need to cross into other areas, just do your jobs well, and towns should give agencies enough funding to do their job well without having to rely on someone else.
there have been many documented cases where LEO complicate scene (hello, every time a fire chief is arrested of threatened with arrest for failing to follow a LEO order), and my personal experience where a LEO will either escalate a situation and then leave the now aggravated or agigatated patient in the hands of EMS. Don't get me wrong, I like many of the cops who work with us, or don't go out of their way to antagonize patients (or us), and am thankful to the ones who have dealt with those unsafe scenes.
let PD deal with the crime stuff, cities usually have enough stuff to keep them busy. if I need them, I will call them and back out. Very similar to the rural areas, where you have one state trooper covering 80 square miles and 6 towns. do you really want to tie them up on an EMS assignment when all they will be doing is write a report and maybe hold a flashlight?