What you're missing is that the after-school tutoring will also need to be stopped. Either declare it illegal or raise taxes high enough that families will not

What you're missing is that the after-school tutoring will also need to be stopped. Either declare it illegal or raise taxes high enough that families will not have any disposable income left to hire tutors. State-sponsored tutors could then be required to apply for licenses that require them to reserve their hours for the neediest students.