You expose another issue that comes up frequently which is the idea that the cost per pupil is somewhat fixed in a region (for administrative purposes anyway) and so regardless of the school a parent choose for their child, the state should pay that school. As an extension, if the parent would choose to home school, that parent might be paid the prevailing rate for a child.
I don't think that works on a number of levels (again, poor parents probably can't afford to not work for $6k for 9 months of the year). Perhaps combined with other social programs (such as a UBI), this would be more reasonable. I think there would be a huge media backlash over kids who end up with effectively no education due to parents just taking their kids UBI+their UBU+school fees and then letting the kids play video games all day (regardless of whether this actually happens or not). Standardized testing would probably become even more important as a means for the state to make sure that your children are actually being educated.
Public education must be - or at least have the appearance of being - a good deal economically.
http://www.statisticbrain.com/television-watching-statistics...
Perhaps if the average American cut down their TV watching time in half, they'd suddenly have time to spend more on their children and help them through the subjects studied at school.
Going by the provided statistics, is it any wonder Asian Americans (least amount of TV time) do better in school than other demographics? I have no doubt that parents in those households spend an above average amount of time helping their kids with schoolwork and make absolutely sure they don't fall behind.