When the option is some fried food vs a wilted salad with no protein source, it's a wonder that any kid would choose the salad.
I would love to see better options that are both healthy and enticing. Until then I doubt that we will see much change when the choice of what to eat in the lunch room is left to the children.
School food generally has the problem that they made to be cheap, low labor, and lowest common denominator terms of taste, spices and salt. To take Sweden as an example, the cost per serving sit just between $0.6 to $1.2 per student in term of ingredients cost. Even providing an apple per student would cut into that budget.
95% of the student body ate that pizza every single day.
This includes the supposedly "smart" kids in honors classes.
The real food was good! It was fresh and perfectly palatable and varied enough to be healthy!
Instead of eating it, the students literally invented a lie to hype up this disgusting facsimile of "pizza" as good. It was regularly claimed that this pizza came from a local small business that sold pizza. This was flagrantly wrong and obvious to anyone who had eaten that pizza, as they used a sweet sauce that was not used in the school pizza.
But what the actual hell do Americans expect? We spent decades disallowing the government from telling your kids anything useful, we opted out of "Only 12 minutes of advertising to children per hour on TV" because "regulation is bad", we built a society that advocates rampant consumerism to your kid from before they even can read.
Of course they're going to eat the shitty pizza. It's what consumerism tells people to do. In the US, consumerism is a literal lifestyle brand!
They’re rejecting WHAT you offer WHEN you offer. They’re not refusing to eat. If you simply allow them to say no, they get hungry and come back (usually within an hour). Ask them what they want from the available healthy options and feed them that.
In fact you can set this up ahead of time. “Child what are your five favorite foods? Great two of those are special occasions only, pick two more. Great. That’s your list. Here’s the deal. At meal time you can pick one of those five. I promise to make it, if you promise to eat it.” This gives them a feeling of control and gives you an easy answer.
This actually makes your life easier because you can plan ahead and always have that whitelist available. And it’s less complicated because their pallets are simpler.
There is a whole branch of child psychology devoted to this question. They’re not refusing to eat. They’re simply not interested in the thing you offered.
I was at a friend’s recently. He prepared a lovely meal. Fresh caught salmon and great sides. His daughter didn’t eat a single bite. I was slightly offended. I overheard the fight later “dad, I hate fish, you know that” (actually quite reasonable) his reply was “it’s not a very fishy taste” (a tenuous argument). She was hungry before bed and did eat. The whole mess could have been avoided by not trying to feed her something she hates. I then watched for the rest of the weekend. Every time she was offered something she liked she ate it no problem.
This does of course assume that nobody else is undermining you by offering them junk when they get hungry after refusing a meal.
Doesn't mean we shouldn't try to offer healthy option, but just that those would have a limited impact on obesity, expect for maybe calorie deficit if they choose to forgo breakfast or lunch