Perhaps you misunderstood me. Doctors and fire departments don't eliminate the need for private ownership of first-aid kits and fire extinguishers. The reason the latter are still needed is that in many cases a layman's response to a situation, executed immediately, is more necessary than a professional's response, executed later. If someone is in a major accident, a layman with a first-aid kit isn't going to eliminate the need for medical attention. If anything, the person with the first-aid kit will 'increase' it [by keeping the patient alive long enough for such attention to be worthwhile].
Police, likewise, do not eliminate the need for armed citizens, but armed citizens are not a substitute for police. Armed citizens, however, can help the police by staying alive so they can give the police the information they need to catch their would-be attackers.
Stay Safe !