Of course you are right that provided identical environments smart and average children cost the same, but since smart parents tend to earn more, smart children cost more.
Non-smart child of smart parent costs even more - on tutors and such to raise the kid.
That is not smart children costs more. That is ambitious/smart parents spend more on children. The cost of smart child here is merely function of correlation with parent.
The reason for the correlation between child raising cost and intelligence is there is a strong correlation between intelligence and income and between the intelligence of parents and their children. Smart kids tend to have smart parents who tend to have high incomes. Of course there are many exceptions, but we are talking about group averages not individuals.
In that context, my response that "The cost of smart child here is merely function of correlation with parent." is valid.
Another major factor contributing is children are very expensive and smart children are much more expensive to raise than the average child.