Wouldn't it just be easier to just provide lunch to all enrolled students? All the money spent on determining and reporting on eligibility could instead be used to just provide the meal. That way no child is shamed or singled out in any way because of their parent's economic status. 

I honestly think the cost of providing every child's lunch would be about the same as maintaining and collecting lunch accounts and dealing with the bureaucracy of processing applications for free/reduced lunch and breakfast.