well, im not from us but the cops still carry a gun with them, even if they are called because of noise complaint
It's really just a thing for the plot, just like evil mother in laws and kabedon rarely occure irl
although I'm sure corruption in the system is common just like it is pretty much anywhere
I live in Sweden and I can assure that even though police do carry around weapons they rarely use them. I think it's more important for an officer to know how to act calmly in certain situation instead of screaming around with a gun pointed at a suspect

What kind of cop doesn't have his gun or belt?