This is a good idea gone bad. If the children of the poor are undernourished, but live at home with their own parents, then those parents are neglecting them. If that neglect is unavoidable, then curses on us and we should be moving heaven and earth to address the problem.
But if that neglect is willful, then the answer has to lie elsewhere. There is no more powerful place to civilize a child than the dinner table. Whether the fare is rich or poor, it can be nutritious and well-prepared and served with love. The idea of lazy parents telling their wee ones to go catch a meal in the school cafeteria on the weekends because they cannot be bothered to make Sunday dinner is so disturbing, I hardly know where to begin.
It is not my job to make dinner for my neighbor's child, any more than it is to read that kid a bedtime story or take him to the MD when he is sick. The very worst possible substitute for a parent is government.
There has to be a better way to feed the hungry than by segregating the children from their families.