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If that theory were correct, Asian people would be the least healthy on the planet. When in fact the people of eg Japan have been among the most healthy for thousands of years.
Caucasians - for example in Scandinavia - getting taller did not equate directly to being far healthier than their Japanese peers.
Height increases over time are driven by the type of diet consumed. The Japanese diet did not lead to height, however it did lead to health and longevity.