Those are the results of a study recently published in JAMA Pediatrics, and really, they don't seem all that surprising.
Firstly, the breakfasts were offered to all children, regardless of whether this was, as Hobbits might say, second breakfast.
But more to the point, would anyone expect a not likely to be sating breakfast consisting of cereal, muffin, juice, and milk, to have a positive impact on weight or health (and I should take the time here to point out that the study authors were not in charge of what schools chose to feed their students)?
As I've ranted many times, what a person eats for breakfast likely matters a great deal to satiety, health, weight and what have you. I've also ranted on the dangers of lumping studies of specific meals (in this case ultra-processed carbs washed down with a bunch of liquid calories) and then opining on the benefits of "breakfast" as a meal.
Food insecurity is real, and finding the means to ensure children eat healthy meals is laudable, but feeding children who are already at increased risk of chronic diseases, meals that may themselves increase the risk of developing chronic diseases, probably isn't in their best interest, and given that, as one of the study's authors Kate Bauer noted on Twitter,
"all breakfasts met the federal School Breakfast Program requirements"
it sure makes one wonder whether America's federal School Breakfast Program could stand for some revision?