But why were they aggressively selecting for tall stature? Perhaps because they were on average shorter than rest of Europeans, so they felt there is something wrong with them? Which isn't unbelievable, I've seen shortest girls demand the tallest men.
So when nutrition improved those already tall genes which were there, got time to express themselves to the fullest.
Here is some acecdote:
In my village, people mostly select average height partner. And tall people aren't considered more desirable. No one compared height or thought of it as some advantage but when men from other tribes started appearing near the village, suddenly they started thinking of how to increase their height, some are now drinking gallons of milk in effort to improve their height because they are lagging, while women want the tall men now. My grandma tells me, they never thought about "height" as a trait they select in their partner, they never thought about it. To her, any man who was average and could work on farm (not crippled), was not very ugly was a good partner.
Three sons - 6', 6'3" and 6'4"
If the height differences were adjusted for income etc, it would be convincing. I didn't read the OP. Did they do that?
They did compare them to other populations at the time. Unless the Dutch were especially under-nourished, then the effect seems reasonably well-founded.
Imagine if you've a goal to increase height of people from 165 to 190cm with minimum number of generations. How will you go about it.
Easiest and fastest way is to have two tall parents breed. You'll see it happen within 2 generation.
Now, if you improve nutrition of people who are 165cm today. How many generations of better nutrition does it require to make them reach 190cm? Certainly more than 2 generations.
Point is that, if you think "sexual selection" is not fast enough to take people from 165 to 190 within few generations (as is the case with Dutch) then better nutrition certainly is not either.
Cattle/pet breeder do it all time.
We can get a precise idea about this since it shows up in the genetic record and over the long term it's under half. A lot more men than you think are cuckolds.
How do you know most males get chance to breed in our society?
Just because a lot of men end up married and have kids to show doesn't mean they are their biological kids.
These days I see single moms are marrying guys who simply take care of the kids they already had.
Meanwhile Denmark sperm export is doing good.
These days many people are getting suprize on 23andme when they come to know about their lost connections.
And but how do you achieve that just using nutrition?
Effect of nutrition on height is overstated. Unless someone is malnutritioned, their height won't benefit much with better nutrition
We can even see this in cattles, if you start with a short cattle, no matter how much you feed it for generations, they'll still he shorter than one you can get from tall breed.
(Yes, I am aware…)