The fact that you think this is a seriously practical suggestion shows that, very fortunately for you, you have no idea what goes in a household like this. I say this with sincerity, it's a good thing that you don't realize the problem with this suggestion.
Agree - if my 10yo son was in charge of getting his own food for school from our well stocked fridge, I know he'd struggle to get any kind of balance.
I know from friends in education who see kids come to school who have had to try to find food to bring in. I live in a relatively well off area but kids still come to school with stuff like just dry bread or a single cereal bar as there just isn't anything to hand for them to bring in for school - looking after their kids welfare isn't a given for a sad and sizeable minority.