Yep, that's an area I'd expect to be expensive.
FWIW, in the far northwest Milwaukee burbs, my property taxes are about $5K. And I hope at least 80% goes to the school district... The only other thing property taxes fund here is the municipal government, which in our case is far smaller than the school district. 21 total (full and part time) employees for the village, 311 for the school district.
Um, no. They get the same $ per student, in theory... But for the ones that get kicked back to the public system after count day, the private school gets the $ and doesn't even have to have a student, while the public school gets $0 and has a difficult (ie expensive) student they have to educate.
And of course they get worse results, they get the worst students. The ones that have severe "issues" and require an aide are particularly expensive, while the model students the private schools like to keep have a below-average cost.
And the public schools are not spending more money per student - They get less money per student because they're getting more students after the funding gets dished out, while the private ones get fewer students and keep the money.