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This misses the important point that the recent increase in average height over the last century or so (basically since the end of the Industrial Revolution) is actually a return to form for humans.
Up until about 10k years ago average height across the globe was closer to 6f. The rise of agriculture and shift to an agrarian lifestyle away from hunter gathers saw a massive drop in protein consumption by the average person. Less meats and proteins and fats and more carbohydrates resulted in a drop in height over a period of about 2k years. To the averages we saw up until about 1920.
We ate more often, but of lower nutritional value so our average heights dropped massively.