Here is a key paragraph from early in McCarthy's article (emphasis added):
In his 1949 State of the Union address, President Truman noted that to fill the needs of millions of families with inadequate housing, “Most of the houses we need will have to be built by private enterprise, without public subsidy.” Nearly 70 years later, our collective failure to solve the affordable housing deficit may stem from wrongheaded analysis of the problem, and the conclusion that market-based solutions can be designed to solve the mismatch between the supply of affordable housing and demand for it.
McCarthy, in other words, is telling us that "the market" has not (and will not) ever solve our affordable housing problems. Building more houses, in and of itself, will not result in new housing that is affordable to average and below average income members of the community.
Perhaps it is time that we question the conclusion that market-based solutions can address the challenge of sheltering a country’s population. Truman concluded that “By producing too few rental units and too large a proportion of high-priced houses, the building industry is rapidly pricing itself out of the market.” But Truman was thinking about the market for shelter, not investment. Remarkably, the number of housing units in developed countries significantly exceeds the number of households. In 2016, the U.S. Census estimated that there were 135 million units of housing in the country and 118 million households. One in seven housing units was vacant. This over-supply of housing characterizes every metropolitan market in the United States—even markets with extreme shortages of affordable housing. In 2016, 10.3 percent of housing units were vacant in New York, 6.0 percent in the San Francisco Bay area, 8.2 percent in Washington, DC, and a stunning 13.7 percent in Honolulu. The problem is that many households have insufficient incomes to afford the housing that is available.