What’s at core of the affordable housing problem?

I stumbled on this excellent piece “The Zen of Affordable Housing,” by Dan Bertolet, a recovering electrical engineer, who blogs at Cititank.org. In it, he tries to debunk some myths and expound on what he considers truths of cities, housing and the market. Example:
The urban density debate is over. An ever-growing mountain of density research unequivocally demonstrates the benefits associated with energy, greenhouse gas emissions, water, habitat, farmland, economics, human health and safety, etc. It’s not hyperbole to say that in America, our future prosperity will depend heavily on the densification of our urban areas. Accordingly, high-density housing should be recognized as a public benefit in itself. 
But his final point is one that, in my observation, is the core of the problem and gets overlooked by virtually all the interested parties in the affordability debate. It’s all about income. If your income is too low, it’s tough to afford a place to live: 
Income inequality is the core reason why housing affordability is such an intractable problem in the United States. In pretty much every other industrialized nation on earth, greater redistribution of wealth helps ease the problem of affordable housing. This includes social investments that significantly reduce other major household expenses, such as health care, education, childcare, and transportation, thereby freeing up more income to pay for housing. Here in the U.S, we will be beating our heads against the wall forever trying to provide enough affordable housing to make up for this underlying inequity.