So ban all mass-produced bread, especially whole-grain?
AIUI this is because the whole wheat flour tends to impart a bitter taste, so the sugar balances it. The sugar also enables the yeast to raise the bread faster, helping mass production.
Having said that, I see your point that setting too low a threshold might be unnecessarily onerous on cafeterias and manufacturers. Perhaps a threshold of ~1g sugar per slice would be more reasonable?
That's not nothing of course, especially for a school trying to minimize food costs. Many schools (like the one I attended growing up) procure the cheapest possible USDA/NSLP-approved product.
But kids at these sorts of schools seem like they'd see the greatest benefit from this sort of legislation to raise the threshold of what constitutes a healthy lunch.