School Lunch! Why not for all?

 Sources:

https://www.nber.org/system/files/working_papers/w23218/w23218.pdf

A study done in 2017 in California found that students at schools with healthier lunches scored moderately higher in testing. This difference comes at a very small price, costing less than other interventions such as creating smaller classroom sizes. It is common knowledge that better food quality results in better outcomes for students. So, when a child is unable to pay for their balanced meal why is their hot lunch replaced with two slices of bread and a cold slice of American cheese. 

Not only is that a lower quality meal, but the act embarasses the child. Would this not lead to reduced test scores and indignation for the school system? Is the parent's inability to pay for a child's meal worth perpetuating a cycle of poverty?