I agree with most of your statement except this: Good for you food is the most expensive.
This is a common perception, but it's incorrect - and usually the ones who cite the cost as the root of the problem (not saying you, not saying you - it's in general) are eating at McDonald's three and four times a week.
My DH and I had a conversation about this one night and we came to the conclusion (and I don't mean the federal school meal program - THAT needs to be scrapped - if the Feds wanted to negotiate better contracts, they could - look at what Medicare says is allowable and what the pt is charged if you need a nearby example, because that's Federal negotiation at it's best) that this is bogus. We even designed a shopping list and concluded that a family of four can eat reasonably healthy on about $65 a week. YEP, $65 A WEEK.
On average, the cost of McDonald's for four people, even just three times a week is $72, using $7x2 adults and $5x2 kids as a baseline figure. Fast food is expensive.
A bag of oranges is three bucks. A bag of chips is three bucks. I can keep going from there...
If the Feds weren't so lazy - and yep, I do mean lazy - they could negotiate contracts from food vendors and fix that abhorrent program. They won't, and yet when my sister sent her child to school with a PB&J, a juice box that was 100% juice, fresh orange slices, and a small cookie (all organic, by the way, and all without preservatives or artificial colors because my niece has crazy dye allergies, the school system forced my niece to buy a milk with money she didn't have on her and sent a letter home to my sister warning her that if the kid came to school without a dairy source or a verifiable allergy, she would be forced to either buy it at school or toss her lunch in the trash and buy one from the school.
Rightfully so, my sister went ballistic. Are you KIDDING me? Kiddo hates straight milk (so do I! Can't stand it - I have dairy in lattes and in my cereal bowl and in yogurt!), so the teacher loaned her whatever the cost was and Kiddo, who then tried to give the milk away and was unsuccessful, ended up throwing the milk in the trash.
After my sister threatened to go to the local TV station and blow her cork, the school system (yep, it went to the county level!) did the intelligent thing and dropped the matter.