I don't think nutrition is as important as you think.
It's 99% genetics. I go to a school with a diverse population White, Black, Asian, South Asian. Everyone's had good nutrition since it's a sports academy school in a good neighbourhood so no one misses a meal, everyone is educated on nutrition etc.
All the white guys grew to be as tall as their dad or 1-3 inches taller.
All the black guys grew to be as tall their dad or or 1-3 inches taller too.
All the south Asians Indians/Pakistani grew to be as tall as their dad or 1-3 inches taller too [EVEN THOUGH most of their parents had bad nutrition growing up in Asia so having much better nutrition only helped them increase their height the same amount as white and black people.
BUT Asians like Chinese, Japanese, Vietnamese must have some sort of hidden height gene because all my Asian friends dads are like 5ft 2 but my friends have grown up to all be like 5'10+
History: China etc were all rich countries hundreds of years ago with good nutrition whereas South Asian countries have never been rich so I think all these Chinese people gained the height gene like Europeans but the past 200 years they've been poor with bad nutrition so didn't maximise their height until now.