John Oliver was making fun of Jamie Oliver, but I watched both the UK and US versions of Jamie's School Dinners, and they did address all kinds of real problems on those shows. The core point is that you can't change the food without providing a lot of context and support OUTSIDE the lunchroom. Kids will rebel and the parents will back them up. To have even a chance of success, you have to integrate lunch into the curriculum; gradually teach kids about one or two unfamiliar foods at a time so they can see, touch, and taste; get kids involved with growing, chopping, and cooking ingredients; educate the parents too -- it requires a massive cultural shift.
In the UK, it was wild -- 300-pound parents were sneaking McDonald's to their kids while demanding to know what the problem was with the old school menu.