My issue is that "locally grown" is just one of those buzz catch phrases that sounds good but is essentially meaningless. It's impossible from a practical point of view out here because 95%+ of the farms in California are now owned by huge corporations that would laugh at anyone trying to make small orders for some school or local farmers market. You want their stuff? Fine, order it in huge batches from their central processing facility nine months to a year ahead of time like everyone else.
Now we do have Farmers Markets but they have the exact same stuff as the supermarkets since they have to use the same suppliers. So, in essence, the only way a school could use locally grown food would be for the school to buy some land and open it's own farm. Which I don't see happening because viable farm land does not come up for sale much unless some developer offers an obscene amount of money so he can build homes on it.
Seems to me that you're taking what might be the case in California, and applying it to the entire USA when it may not be applicable... There are quite a number of smaller farms in my state -- they are not owned by huge corporations -- and purchasing solely from them can more than easily stock my entire produce need, and then some, with quite a bit of diversity.
You're also making some assumptions about supermarkets and where their supply of produce comes from -- have you ever actually looked at where tomatoes come from when you're buying them in November? How about grapes? Lettuce? Cucumbers? Bell peppers? One of my local grocery chains prides itself on using local growers instead of national (or international, as the case may be) supply chains, and in the course of proving that labels every produce bin quite clearly with exactly where the item was grown. In summer, 90% of the produce has US (primarily WA, OR, ID, or CA, which are local for me). In winter, however, that percentage shifts drastically to a good 75% or more of produce items being from Chile or Mexico simply because the growing season here in North America limits what can be grown year round. Sure, the cabbage and potatoes are local year round, but tomatoes, cucumbers, bell peppers? Nope.
How much fossil fuel do you think gets spent shipping tomatoes from Chile to NW WA? Hm? And how early were those tomatoes picked to avoid them going bad on the journey? How much nutrition from those tomatoes was lost due to being plucked off the vine 2 or 3 weeks early, when they were still mostly greenish? Do you know?
In addition to that, do you know where schools currently purchase their produce from, and in what form? Remember, we're talking about the USA school system here -- that's the same USA that had ketchup classified as a vegetable so that schools could have an easier time meeting "nutritional standards."
This blog:
http://fedupwithschoollunch.blogspot.com/ is a bit of an eye opener about what's being served to our children for lunch. Take a look at how much of that is pre-processed, preservative laden, high sugar content, pre-packaged, food from FSM knows where. Are you really going to argue that those school lunches couldn't do with a little bit of locally grown fresh produce to make them A) more healthy, B) tastier, C) cheaper, and D) more appetizing?
School lunch is no longer what it was when we were kids -- i.e. reasonably healthy full meals.