How about home-schooled children?
You could do some nice field trips for $5000.
Especially if you have five or six school-aged children. “Guess what, kids ... we’re going on a two-week history cruise in the Mediterranean. Be sure to take notes!”
However, if the state included homeschools in “private school,” they would still run into the money problem. The only way this works out financially for the state is if they get students who were in public school, out. Even too much of that would be bad, because the public school system exists to expand, and if too many students leave, the public eventually notices that they’re spending more for less.
If we recall that the public school system functions for the benefit of its employees, rather than the benefit of its “customers,” it all makes sense.