If government has any "useful" purpose, then it's coordination. In the two examples given, it's coordination to avoid negative effects of economic externalities

If government has any "useful" purpose, then it's coordination. In the two examples given, it's coordination to avoid negative effects of economic externalities. In the case of firefighting, the negative externality is that burning house may present danger to other houses nearby it. In the case of global warming, the negative externality is CO2 pollution from burning of fossil fuels.