I've learned a whole lot about nutrition and hormones in the past year or so and I'm nearly fully convinced that even within the western 3,000 calorie/day diet there is margin for change in total growth.
First, you can find various studies online, I'm not sure how many, showing that giving Letrozole to teenage boys causes an increase in total growth as measured by final height. Letrozole is an aromatase inhibitor, used for breast cancer. In people, aromatase is an enzyme in fat cells that converts testosterone to estrogen. So for fat teenage men you expect them to grow less tall, and I think these Letrozole studies are a good means of confirming that expectation. Note that estrogen is one of the contributors to ending growth, as it shrinks the growth plates between your bones. When your growth plates are gone, you stop growing. So definitely, pre teens and teenagers should have very low levels of bodyfat without being malnourished.
I wasn't an obese teenager, but I was fat, and I did stop growing at 14 or so when I reached 5'11. Perhaps I would have grown more afterwards with lower body fat, hence lower aromatase, hence lower estrogen and greater testosterone, that's what the Letrozole studies found.
I think when/if I have kids I'll do what I can to keep them well fed but lean. That means less bread, less sugar, a lot of high-fat and high-protein foods, and putting them in a lot of sports early on. I was in no sports unless I went and played basketball or soccer myself.
Separately, constant feeding/snacking is known to inhibit human growth hormone in adults. I don't know if it does so in kids, but it's plausible. In Spain, where the culture is to constantly eat in many meals a day, the average height for men is ~173 cm, very short.
Separately, I was in Sweden recently. The people there are taller and slimmer. You might say "that's genetics !!" but the rankings of tallest countries in the world have changed over time. Americans are actually growing shorter. The Dutch used to be very short. Anyway I'll tell you about the diet there. You know how we have krispy kremes in our petrol stations? In Sweden, they have salad bars. I'm serious, I have a photo if you want. You know how some restaurants here give complementary bread, oil, vinegar, and butter? In Sweden, the salad bar is complementary. Also, the largest meal of the day is lunch. Typical lunch is fish, bread, butter, potatoes, sauce, vegetables. They rotate the fish so that you use from many species of fish over time. The desserts are different from American desserts too, more butter less sugar.
