> The issue with that theory is that height is significantly more correlated with labor market outcomes for men than for women.

How about cognitive abilities? You'd need to state that there is no (or less) difference in those between the two genders in order for this to be a valid counter argument.

> correlation between height and cognitive ability existing in a world where children suffer poverty/malnutrition/exposure to lead does not imply

The paper uses UK and US data.