Of those listed, the following are not fruits or vegetables: nuts, seeds, peanut butter, olive oil, legumes, and lentils.
The issue is one of nutrients - just as an example, take calcium. Is there calcium in raw spinach? Sure. It's one of the better things on that list of foods for calcium. But to get the adult RDA of calcium, you would have to eat roughly a KILOGRAM of raw spinach, 33 servings by the FDA's admittedly wussy count. IIRC, kids may need slightly more calcium than adults due to bone growth, but I don't have the numbers in front of me and it's close so we can ignore that for the time being.
Now, how are you going to get over two pounds of spinach down the mouth of a small child? I don't care what you do to dress that leafy morass up, that just isn't going to fly. With a non-vegan child, 3 cups of milk (one per meal) will achieve the same 100% RDA with no pain and no fuss.
Analogous arguments could be made for other nutrients that vegan foods are short of, protein being the most obvious.
Now I'm certainly not vegan, but I think what happens to most vegan children is that their parents just sort of pay lip service to the nutrient issue, and they never get enough of several key nutrients. The result is small, weak, low bone density children that will pay for all those things later in life.
The problem with heavy children is mostly quantity of food, not food type. While changing to a vegan diet may inadvertently decrease quantity (since very few people could stomach that much spinach
), you can achieve the same effect in other ways (say, by teaching your kids what constitutes a healthy quantity of food and paying attention to their weight) without depriving kids of essential nutrients.