The point is that fire-fighting began as a private function. Largely volunteer in the U.S. In London, fire brigades were hired by fire insurance companies. As I will argue below, the latter seems like the right model.
the definition of private property rights, was perhaps inadequate for private enterprise. The problem was that to provide effective fire protection for even a part of the population, all fires had to be fought promptly to prevent their getting out of control. Under the existing legal framework there may have been no reason for any given person to pay for the services of a fire department since, if enough other people paid, the service would be provided free.
good old-fashioned rent seeking accounts for the rise of public fire-fighting. It explains as well the survival of an entity that, more and more, is losing its raison d'être. Modern building materials are relatively fire-proof, while clothing and other fabrics are flame-retardant. Municipal codes increasingly require sprinkler systems, smoke detectors and other devices to reduce the incidence and costs of fire. So today's fireman has much less to do.
I am skeptical of the pure rent-seeking story. Anderson gives a lot of reasons that the volunteer system evolved toward the municipal system.
I do not know what to make of a volunteer fire department that is supported by the city. Is it a private institution or a public one? It looks mostly public to me, since customers are not charged for fire-fighting services. It operates on a combination of taxes and volunteer labor. But I fail to see it as a robust private-sector institution.
I think we could have competing, private, for-profit fire companies. As I argued earlier, they would charge membership fees. They could charge higher fees based on risk. But with competition you could not charge a fee based on perceived ability to pay. A competitor would undercut you.
I think that the solution to the problem of how to get people to pay the membership fee would come from fire insurance. I would assume that if you want to get fire insurance, the fire insurance company will be much more receptive to writing a policy if you maintain your membership fees. Mortgage lenders, in turn, will require fire insurance. As long as the vast majority of people who own their homes free and clear also obtain fire insurance, not many people would go without fire protection in this scenario.
If someone goes without fire insurance and without fire protection, then I do not see why taxpayers should have to do something for them in case of fire. Such a person owns their home free and clear, so presumably they were not impoverished before the fire. (This is in the theoretical world where fire protection is required by providers of fire insurance, which in turn is required by mortgage lenders. I do not know about the recent example of the guy who didn't pay dues to the nearby municipal fire department and consequently had his house burn down. I am thinking, though, that if the house had a mortgage, the mortgage lender probably wishes that it had required dues payments be placed in escrow so that the lender could have made sure that the dues were paid.)
We could have taxpayers pay to put out the fire in order to protect neighboring properties. We also could have a law that says that if taxpayers need to pay to put out a fire on your property to protect neighboring properties, you can be stuck with a hefty bill from the taxpayers.