Private school savings:
Less Administration
No Unions
Less grandiose facilities
Focused curricula
No Featherbedding administration.
FWIW, in British Columbia, Canada, we have a system whereby about 60% of the cost of public schooling is covered by the province. The rest of the cost is covered by tuition. That is how our small private religious school operates.
Our school has reasonable tuition of about $4000 per child. How it is done is the compensation package is way way lower than the public system. The teachers are paid around $40,000 with no pension. In public school I believe starting wage is $49,000 but add to that $15,000 in benefits.
The teachers take that lower compensation because they care about getting the children having a Christian education. Also, in our coastal city, finding a full time job in the public system is next to impossible.
The teachers unions of course despise that private school get any money.