Since nutrition standards were strengthened in 2010, eating at school provides many students with healthier food than is available cheaply elsewhere. Plus, reducing stigma increases the number of kids getting fed.
By 2017-2018, foods consumed at schools improved significantly and provided the best mean diet quality of major US food sources, without population disparities.
The large improvements at schools were associated with increased whole grains and less saturated fat, SSBs (Sugar Sweetened Beverages), and sodium.
You didn’t read the article.
It linked to a study that refutes you.
Source: https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2778453
Um I read the menu at my kids school daily. Read whatever study you like.