The Obummer food push didn't work because it pretended kids like herb roasted baked chicken, and other things that are made more for adults. Kids have developing palettes, and they will just not eat instead of trying things. And there's nothing wrong with that as long as it's not exclusively tendies for every meal. Kids like ketchup on hot dogs, as they age they like mustard and other toppings, t's just something normal.
So to just have simple rectangle pizzas, but made with real cheese, tomato sauce that is not 40% sugar, and pepperoni that isn't dog food reject level, this is good, this is better. Making food better is really a situation of just small changes here and there will have an immediate noticeably better effect cumulatively.
I'm not sure about kids being as picky as people think they are. Yes they like sweets, have little impulse control, and enjoy junk food. But in plenty of cultures kids eat largely the same as the adults do. At most they'll complain about the vegetables because kids are more sensitive to bitter tastes (they're not just exaggerating, it's a developmental thing).
I've prepared food for my "picky" nieces and nephews and as long as it doesn't taste like shit they never complained and ate up without issue after being told I don't have nuggies. Some stuff they didn't like as a matter of preference but that's normal for adults too.
These are kids who eat cereal, trendies, kraft Mac n cheese, etc at home because "they're kids so they're more picky". And will whine to my sister about not liking whatever before having tried it.
Likewise when I was growing up everyone ate the same dinner. Kids did not get separate food. There wasn't anything I didn't really like except for saurkraut and sausage which I still think is pretty gross except for maybe once a year. And black eyed peas on new years - also gross.
Other than that I just ate normal ass food. Turkey with tomato and rosemary, pot roast with potatoes, homemade pizza, some sort of meat with a vegetable and corn or potato, Indian curry. Scrambled eggs or omelettes, sometimes pancakes.
Dessert was rare. Candy and junk food were for family movie nights. I didn't mind either. It was was mainly when I was a preteen under my dad's influence that I started eating more fast food and treats. Of course I didn't complain, but even then I didn't complain when we had normal dinners at home.
However I think having familiar but higher quality (full fat dairy, whole food, no seed oils, no added sugars) versions at school would be a fine compromise. They also shouldn't be giving desserts every single lunch. Many schools give cookies, etc, at lunch from what I hear from parents I know. It's nonsensical and completely unnecessary.