Ok, so answer the question then - what work program would there be for those 12 year olds that cannot function in the company of polite society. Like what kind of work would you have them do and how would you ensure compliance.
Btw. I am not advocating for work programs as a particularly good solution, expelling and letting the parents to figure out what to do with their misbehaving child is a good solution too. School is a privilege for smart children to study, not a prison for those who do not want to learn.
It's actually neither of those things, because we discovered hundreds of years ago that having an educated population is good for everyone. No, it's not a prison, but it's not a privilege either - you have to be in school until certain age. Work is not substitute for education.
And schools have been able to deal with "brats" for over a century without kicking them out of school.