It's a dystopian hell only a libertarian could love.
Privatize essential life safety services? Because that has worked oh so well for healthcare.
The standard line always is, "we will do it better than X" - well fix current government run healthcare first
The NHS in the UK has its problems, but they are not nearly as bad.
(I don't know which country's system is the best to look at as a good example of private health care. Perhaps the best parts of India? (India ostensibly has government healthcare, but it's so bad that everyone who can afford it gets private health care. I don't know how bad the interference is.)))
Not only that, but fires spread, they need to be caught early, and they're preventable. It's not just a matter of performing a service for one home at a time if they catch on fire, it's a matter of performing a public service to reduce the risk of fire, enforce building codes, minimize damage caused by fires, and save lives. This is something that requires a community effort, and needs to cover the entire community uniformly.
Before being concerned about firefighters, it seems to me that we should be more concerned with improving the conditions for loggers and garbage collectors which have much greater work related risks.