https://en.wikipedia.org/wiki/Broad_Street_Riot
Here is a comedian's take on it in podcast form: https://thedollop.net/wp/episode-138-dollop/
This creates the perverse incentive to demand an outrageous price so they can get an property for cheap. Next step would be setting fires to buy even more property.
Now, if two crews showed up and bid against each other, things start to get interesting.
It also means it might be that nobody shows up, because it's a holiday, so nobody was on duty.
Well surely public services are more incentivized to display this behavior
Sabotage and physical fights broke out between fire companies while fires burned. That's a pretty gritty situation.
Allowing fire sales gives way to perverse incentives, like the profitability of arson and predatory pricing of fire fighting fees such that certain portion of victims will always have to sell their property at a discount.
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.
(I certainly prefer publicly funded fire service)