The median home price in Dallas is comparable to most cities outside of LA and SF in California, and higher than that of Chicago. Austin? Don't even bother looking it up. You should have said Houston. :)
The fact remains that Dallas and it’s surrounding suburbs is a vastly more egalitarian and less stratified place than SF or NYC. It has tons of affordable areas near the city. A key problem is that the industries powering NYC and SF (tech and finance) are massive drivers of inequality. They create a huge upper middle class that just sucks up all the resources. That’s exacerbated by the difficulty of building housing, but both sides of the equation are the problem. Northern Virginia where I grew up is a place where it’s easier to build housing, but has a similar problem. The middle class has been driven out as knowledge industries have taken over.
Iowa is even better lovely because there is basically no upper middle class. Even the farmers who might have tens of millions in land are pretty cash poor.
New York is bad. California is pretty rough too. But Louisiana and Mississippi both have higher Gini coefficients than California. It's not tech and finance that made Louisiana and Mississippi the 2nd and 3rd least equal states in the country.
Further: if you dig into Gini by cities, your hypothesis gets even weaker: one ranking I found goes:
1. San Juan
2. Atlanta
3. Miami
4. New Orleans
5. New York
6. Cleveland
7. Cincinatti
8. Dallas
9. Tampa
10. Chicago
(I'm playing with the actual ACS data from Census.gov now, but haven't figured out how to get it broken out by major city; if you do by "places", which include every city no matter how small, the leaderboard is dominated by small rural cities).
No California city even appears in the top 10, and the list is dominated by non-finance-centers in red states.