Earlier quoted context omitted.
How about homeless high school kids? Or high school kids with one parent who are helping to supplement their household income?
There are other programs out there to support the homeless and single parents needing financial aid for their kids. A high school kid making money regardless of his family's wealth is making money as a supplement to what the parents or guardians should already be receiving from the government or otherwise, assuming they aren't emancipated but that is a very special case. If the parents can't afford to meet the basic…
There are frequently waiting lists, restrictions (my favorite is disability, where you are not allowed to work, but are given barely enough money for yourself to live on), and miles of red tape associated with government subsidies. There's also the very real cost to the pride of the entire family associated with these subsidies.
> why should the state allow for a child to remain in that home
Because moving a child is incredibly traumatic for the child and expensive for the state?