In theory, all of this also applies to a public "firefighting department", no? They too could do a really, really poor job. If this is the culture in a society,

In theory, all of this also applies to a public "firefighting department", no? They too could do a really, really poor job. If this is the culture in a society, where people want to screw each other over, you are likely to get this poor outcome regardless. But suppose that you have an honorable firefighting department run by an honorable man. Why could he not have set up a private firefighting company instead, doing pro bono work when required? Given the honorable behavior of his company, why would consumers not want to prefer him for insurance than shady competition, which may be cheaper but is also more likely to screw you over when you most need them? Government-run agencies can be good or bad; private companies can be good or bad. There is no silver bullet and much depends on the prevailing culture. But government can use the threat of force to compel you to pay for their services. If a private company attempts the same, we would call it an organized crime group.