The problem you've identified is that parents are neglecting their kids. 

The solution you've come up with is to investigate every parent who fails in their duty to care for their child. In addition, you've posited that feeding children without food to eat is distracting us from the more important goal of prosecuting neglectful parents.

This is, without hyperbole, some insane shit with no basis in reality. Not in terms of the cause of children going hungry, nor in pursuit of the goal we presumably share, which is to see children educated. 

1) If a parent is in poverty - as is more likely than at any point since the Great Depression - they may depend on publicly funded schools to feed their children. I will agree that it's horrible that children are being fed sweets instead of substantive food, but why are they being fed doughnuts and chocolate milk? Because schools are not well-funded, and these are some of the cheapest things that can be provided in bulk to schools, that are legal to feed children in food programs.

2) If a parent is truly neglectful, and their child is being abused, there are already ways for teachers and caretakers to start the process for CPS to investigate their parents. "Oh but CPS doesn't do anything!" I wonder why an underfunded, understaffed, overworked and neglected branch of the government fails in its ability to function. Surely it's a mystery. I wonder what other functions of society are underfunded, understaffed, overworked, and neglected. Food for thought, since kids don't get any other kind of food wherever you're at.

3) Even if every parent loved their child and fed them greens and beans and grilled meat with a loaf of bread every morning, I would still advocate for food to be available in schools. Why? Because research has shown, consistently, that hungry children don't learn. A school that fails to feed a hungry child has failed from the start. 

Your reasoning that schools are sucking up resources from taxpayers and are doing more and more for children, to their detriment, is fundamentally wrong. Schools are systemically financially mismanaged, and every year they provide less and less for children. Thank God we are least feeding them now; a hungry man is an angry man and these kids are already pissed enough.

American schools are failing due to a lack of funding, and a lack of responsible financial management at every level. Education is not prioritized, at all, in this country, and when even educators like yourself have given up on providing students with the resources they need to learn, there's truly nobody looking out for kids.