I went to a few schools, including one in North America (public school system), one in Continental Europe (private) and one in the UK (private). Honestly, the Continental European one was streaks ahead of the other two which were pretty comparable. The latter two were both boarding schools and the one in the UK served a very similar menu to the school in the US, unless there was a parental event or another event going on in where there were leftovers.
The menu for breakfast was always cereal or toast with a cup of juice.
Lunch rotated but there was definitely Burger Wednesday, Pizza Thursday and Chip Shop (Fish or Sausage) Friday every week. We did get something that vaguely resembled a roast on Sunday and I cannot remember the rest of the week. We did have a salad bar but it was never fresh; all vegetables were frozen and reheated (grim) and usually it was just peas and carrots, or peas and corn with some form of potato. Or rice, I think we had rice occasionally. I cannot remember what the evening meal was because I basically figured out it was better to cook a simple stir fry or similar in the evenings in the boarding house as we had a couple of hobs we could use. In the boarding house we had access to crappy white bread, jam, margarine, and milk - we could take as much as we wanted but there was an allowance of what each house was given each day.
In Continental Europe breakfast was decent cereals or porridge, you could mix your own muesli, croissants and pastries, cheeses and hams plus as much fruit as you wanted. Lunch (as a boarder) you could either take your own packed lunch, or, as most of the school did, you sat down for a proper meal, starter, main, and desert if you wanted. There was a long rotation period - maybe 4 or 6 weeks and everything was cooked fresh, and sourced from fresh ingredients. Some of the mains I remember were Horse (!) steaks, three vegetables and steamed potatoes, freshly made pizza where you could chose your toppings, Risotto, Pasta, Pork medallions, and lots of vegan options as well. I think we had three or four options for mains a day plus sandwich and salad stations. Dinner in the evening was always a home-cooked meal in the boarding house (there were not as many boarders so perhaps this is why that happened).
The variety of food I could get in the US school was far better than in the UK private school - but the European school topped them both. Needless to say there were virtually no behavioural issues at the European School, very little class disruptions, and people rarely were ill.
At the end of the day school food come down to funding and cost cutting and many schools simply don't see it as a priority, which I find is incredibly sad.