Nope, they don’t. It’s not just one opinion either. There have been a number of rulings over decades. The Court basically says that police have a general duty to society at large, but there is no duty owed any individual. In other words, if you call the police because someone is breaking in your home, you had better grab that .44 because they have no legal obligation to try to protect you.
I understand your statement completely. They can not be held accountable for what happens before they arrive, thus arm up and be prepared. But if you call for help and they refuse to act, not because they were busy at another crime scene, but because the court says they “have no duty”, then they should be in the unemployment line within 24 hours.
Not having a “duty” implies they cant be held accountable for outcomes where they weren’t on scene. It does not mean they can just not show up for work.