It's actually cheaper to own in many areas than to rent. What stops most people is their inability to save for a down payment and/or obtain a reasonable interest rate on their mortgage, both tools used by banks to hedge against the risk of lending. I'd argue that measures of that risk are somewhat arbitrary and reflect an institutional lack of faith in Americans' creditworthiness. So it's not that people can't own homes because they lack wealth, it's that wealth is hard to come by because they're not allowed to own their domicile.
Surely this is a result, not a cause? You have to clear a substantial wealth hurdle to get a mortgage.