It's all well and good saying you can use fire crews based in the city, but what happens when there's a major incident in the city? Who will then fight the fire when someone runs off the end of a runway?
When fire crews attend an incident at an airport now the airport shuts as the rescue services are already occupied with another incident even tough runways may be clear. Are you suggesting airports shut every time the city based fire crews are out on a call?
Furthermore they are all first aid trained and have some equipment to help until ambulance crews arrive - which in the few times a flight I have been on the fire crews were there in minutes, the ambulance a lot longer - 15 minutes recently.