We need them to protect ourselves. We need them to ward off criminals. If you think that the police will be there exactly when you need them, you are extremely naive. Society has an average of 1 officer to every 20,000 people. In a lot of municipalities, it's much lower than that.
Most agencies are only able to respond to an incident after it happens.
If some crazed idiot breaks into your house and is intent on killing you, you had better have some form of protection, because your local officer is probably across town handling a false burglar alarm or a complaint about nuclear strikes in Bosnia.