This is nonsense. In every material good, the buying power of nearly everyone has increased in real terms over time, regardless of inequality. It's only in housing, with constrained supply, that inequality can drive up prices; and even in that case, it doesn't actually change the housing supply- if prices are high, that just means a lot of people who want to live there! Inequality doesn't reduce the number of houses.

Building a little reduces prices a little. Building a lot reduces prices a lot. If the prices are very high, then it's very profitable to build, so unless stopped by regulation, you will get a lot of building. Even if building merely keeps the price from going up as density increases, the value provided by living in an area goes up from agglomeration effects as it grows.