If you take away one’s right to support themselves, you have an obligation to support them.
If children could work, they could presumably receive health care. For the sake of argument, let’s ignore the pay check, work experience, and other benefits – and focus on the healthcare. In many cases, parents can not or do not choose to pay for appropriate healthcare for a child. In these cases, the child might be better off quitting school and working to afford the medicines or treatments she desperately needs. But that child is restricted by law from doing so. The government, by placing this restriction, is morally responsible for providing at least that which the child could have achieved on her own. The government should provide health coverage for any persons restricted by law from the work force.