That doesn't account for the access driven by the decrease in the price of housing that comes from removing the artificial credit subsidy. What you might call a "second-order" effect, though because it's an effect of "doing nothing" it's both more natural and more efficient.

If anything, driving up prices(by subsidizing credit) such that houses can only be bought on credit and not outright does the most to increase housing inequities! Cuz we all know how that shit works :/