Having them working is efficient. Having them sitting in front of a burning house isn't.
Having them sit in front of their cute "fire house" all day is even more inefficient.
And that's what happens, when they are government employees — because each town has its own. The same would be happening, if each town ran its own restaurants — fortunately, the statism has not reached quite that far in this country.
They would do their best to save the burning house, but they would fail every time.
Now you are changing your argument — glad to see, we have the earlier one discarded.
Let's dispense with this new one. Service-providers, that oversell their capacity do not survive for very long either. Customers and insurers track them... Unless, of course, they are government-owned — the "trick" you described can be (and is) used by government-run fire-teams all the time. A mean annual wage of a New York City firefighter, for example, is over $73K, but they will refuse to even try to save your property, under the noble-sounding rule "We only save lives".
So you are saying that insurance is more expensive to cover for the fees in order for them to evaluate and approve private fire departments?
Somebody has to evaluate and approve all fire departments — whether they are monitored by the towns or insurance companies, it needs to be done on occasion. But insurance companies compete with each other and have "skin in the game" — their policies will be too expensive, if they aren't efficient about inspections. If, on the other hand, they are too loose in their standards, they'll lose money paying for houses destroyed by fires.
Town representatives do not have "skin in the game" and are swayed by personal sympathies if not outright bribery, which makes the system less efficient.
My point was just that the city shouldn't be providing a private corporation with free land and free water.
Maybe not. Something can be worked-out — after all, we do have private companies running cables (and even pipes) above and under the streets. Any resource available to government-owned firefighters ought to be — and is — available to privately-operated ones.