It is just like the teacher lower the marks of high flyers to accommodate the least instead of encourage them and guide the way to achieve higher.

Let's go back to the main purpose of the program which is to help provide kids with the vital nutrients (through breakfast), now the reasoning that goes hand in hand here is that poor families are less likely gonna check that criteria, the kids either are having not so healthy food for breakfast or doesn't eat at all

Those things are nonexistant among the rich families. Their kitchen, their fridge stocked with food that are leaps better, they don't just pass the minimum they also overqualify, having access to top shelf stuff. The only issue remains is whether the kids would have breakfast or not. The one other very critical thing is pocket money to be used for recess, the riches here as expectedly won't have a problem but is a concern among the poor.

The isolation argument that people bring up is smth that can be addressed in lots of way, but this one majorly falls on teacher, them to encourage, to teach the lessons upon student. Could just let the qualified students roam around instead of specifying an area, but this one is valid for RMT though