The NYPD and its boosters do not really understand what makes a city safe from crime. They sincerely believe that *they* are the only thing keeping the city from the brink of chaos. They are incorrect about this.
That is not to say that they aren't important. They are, just not in the ways that they think.
My loudest and longest standing criticism of the NYPD is that they do not solve violent crime cases often enough and act like this isn't their fault.