When children see food as 'good’ or ‘bad’ it can set them up for eating disorders.

My mother was obsessed with weight for the entirety of my childhood-- Nutrisystem, Atkins, Weight Watchers, Slimfast, Lean Cuisine, you name it she tried it-- every single dessert was accompanied by some form of "you'll get fat if you keep eating that". My mother's intentions were never to cause me anxiety, but to warn me so I could avoid what she felt inhibited by in her own life (she's always struggled with her weight)--- unfortunately, her obsession with food and dieting negatively impacted me in a significant way, and still does today.

Thinking back-- if I was one of these kids and notices like this were sent home to my mother-- it would have only made me feel worse.

While these teachers are clearly well-meaning, I am inclined to say it's not their place--- a more positive and possibly less detrimental approach would be to reward for good habits, instead of punishment over a single piece of cake.