You are assuming that smart kids are randomly distributed through the population. High income parents have disproportionally more smart kids than average income parents and disproportionally live in above average cost locations.

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.

It started with "Another major factor contributing is children are very expensive and smart children are much more expensive to raise than the average child."

In that context, my response that "The cost of smart child here is merely function of correlation with parent." is valid.