Centralized billing cannot work unless all schools are absolutely equal in tuition and services, which frum schools are obviously not. That’s why it works in public schools.
How will you decide which kids will go to the more expensive and possibly better schools, and how will you decide how much each family needs to pay? Will families with more kids need to pay more? Will families with kids in better schools need to pay more? Will parents be able to choose where they want to send their children?
There are far too many holes in this plan to work.
If I’m misunderstanding the plan please explain, but this doesn’t seem possible in a private school system.