A nice idea, and I want to agree with it. Unfortunately, teachers and firefighters are employed by the state, which means they're not going to go out of business if they're out-competed by superior workers. So there's no incentive to pay more to get better workers, they can just pay the minimum necessary to employ almost anyone to do the job.
We are extraordinarily fortunate to have so many superb minimum wage fast-food workers. Their lower pay simply reflects the happy reality that we're blessed with a much larger supply of them.
If you have better schools the district's property values go up which increases the tax base. Families can and do move across districts to access better schools, so there is competition in that sense. Same with many city services. Firefighters and teachers in Palo Alto for instance are paid well compared to other districts, the schools are some of the "best" in the nation, and property values are high as hell.
While factually true, this is disingenuous, at least in the US. Schools and firefighting services are given out for free, which severely limits the market for private alternatives.
