It actually works the opposite. Families least able to contribute to school funding are allocated more $ per student, such as low-income, or foreign nationals here without papers. OK, illegals, I said it. The higher the % of illegal and low income students in a school district, the more funding they are allocated. This might explain the public employee's position on illegal immigration and social programs.
It's actually cheaper to put a K-12 child through a for-profit private school such as a Montessori School, than it costs to put your child through a public school which are at an operation loss. It's the nature of government bureaucracies run by unions. When you don't need to run operations efficiently, you simply don't. It's not greed, it's sloth. No requirement for exceptional job performance? You get below average job performance if it all pays the same.
Sadly for our state, the education your child gets at a Montessori (or similar), is so much better that you may have a hard time locating a nearby public HS to continue their education, if you need to use a public HS. We had to drive our kids into another city to get a public teaching program that was at a high enough level to avoid them repeating classes. We sent an average kid from Montessori > public high school. 4 year IB grad, AP credits, 4.3x GPA, very high SAT. She shows up at a UC system college, and she is too highly educated. Straight A's as a freshman as she goes into her sophomore year with 21 units of load. <=3 years instead of 4. Her brother is on the same path with high SAT and lots of AP credits.