A big problem is that institutional food just tends to suck. This can be covered up by cramming it with fat, sugar, salt, artificial colors and flavors to make it seem edible. Without that, most people won't eat it unless they're hungry enough to eat garbage, and they certainly won't be happy with it. It's possible to make absolutely spectacular food with healthy ingredients. But that means buying fresh-picked, preferably organic ingredients in a wide seasonal variety, and preparing them wisely. That's difficult or impossible to do on a mass scale. The difference between a Honeycrisp and a Red Delicious is the difference between mouth and trashcan, but that Honeycrisp costs at least 3x as much. Many people just don't find whole wheat very appetizing, but some whole grains like quinoa or amaranth are excellent. These, too, are more expensive and not as easy to prepare.
Now, if you have a sensible setup -- say a Montessori or Waldorf school, both prone to family-style meals prepared in family-style kitchens, often as part of teaching older students how to use a kitchen -- you can offer healthy meals with no more hardship than doubling or tripling the cost, and those are private schools anyway so they're not short of cash.
In a public school, unless you plan to triple the budget, change the food-distribution system, and gut the cafeteria to rebuild it, you might as well admit that you can't be arsed to feed children properly. Because otherwise they're just going to chuck it in the trash unless they are literally starving.