Having a public school system is still cheaper than a collection of private schools and a private school system might even be unworkable in areas that are less populated. A certain percentage of the cost of education goes to operating costs. One large school is cheaper to operate than several smaller schools. How many would be willing to pay more than they do through their property taxes or could afford to?
The voucher system exists in 14 states and based on testing, students attending these private schools are not testing any higher educationally than those attending the public school system.
As much as education is considered a right, it isn't really. The solution to the problem of undisciplined students should be dealt with as it was in the past. Kick them out of school. Have parents sign a contract at the beginning of every school year agreeing that they will be responsible for ensuring that their children behave in school and if their child is a discipline problem, then that child's education is now the parent's problem, not the school system's.