The annualized cost of a school isn't fixed though. Firstly, the capital cost of the older schools may well have been paid off. Secondly, the cost of building one is going to be pushed up by the fact they're competing with expensive premium housing for land, builders, etc. Thirdly, they're also going to be competing with existing schools for teachers and it's not like teachers from outside the area are going to be able to afford to move there unless they're paid an awful lot.
> Firstly, the capital cost of the older schools may well have been paid off.
In the long term nothing is "paid off"; you have to keep up a regular schedule of renovations and renewal projects, or things fall apart. Which is what's currently happening to a bunch of US infrastructure. :-(
As for cost differences, property tax revenue scales with rising land values, so land costs should be a wash (ignoring prop 13 insanity, which from other replies seems like it might be the real issue here). And expensive housing / high cost of living for new teachers is caused by high demand for housing without a corresponding increase in supply. So existing schools would already face that problem, but increasing supply by developing new housing should help to mitigate it.