While the individual questions may be (for the most part) purged of any cultural bias, family income remains the primary demographic correlated with test performance.
Is that surprising though? There's a strong correlation between pay and intellectual ability/education. There aren't many dull, uneducated engineers, doctors, lawyers, or executives.
If intelligence is at all heritable, you'd expect to see this. If educated parents tend to push their own children to become more educated, you'd expect to see this.
I wonder what the chart looks like broken down by where parents went to school or some non-financial metric. I would bet the children of well-educated college professors or journalists also score well, despite growing up with a more middle class household income.
Of course, a correlation with income is likely a spurious correlation from more basic causes. E.g., suppose a poor family whose kids are doing poorly in school won the lottery and suddenly has high income; do we expect that suddenly then their kids will do well in school?
If you look at the Quillet article someone linked to above, most of the high-performing Asians who ace the SHSAT are low-income, so your generalization makes no sense whatsoever in the context of de Blasio's plan.
https://www.washingtonpost.com/news/wonk/wp/2014/03/05/these...
https://pdfs.semanticscholar.org/e7a0/dfdee8ad5b91e1d179e9e2...