Although I ideally believe that the government should not be involved in education in any manner, I wonder if I may have stumbled on a partial solution to public education's ills. If three simple laws were passed, they might allow public schools to eliminate many of the trouble makers, allowing the other students to learn more.
The three step solution:
a. Allow child labour at any age.
b. Allow public schools to expel / suspend any student.
c. Remove legal requirements for students to attend school.
When school is no longer a right, but a privalege, I believe that children and their parents will take it more seriously. By prividing the alternative of on-the-job learning and making it easy to expel misbehaving students from public schools, I wonder if it might improve the motivation and quality of public school students overall. Those that don't want to be in school can go to work instead, and those that do go to school are faced with the reality that if they don't behave properly, they will be involuntarily ejected, keeping them from disturbing the education of the motivated.
I realize, of course, that it is highly improbable that any or all of these three steps will ever be sufficiently socially acceptable, but I believe that they do provide a potential solution short of eliminating public education altogether. They embody some of the key motivating factors that make private schools successful.