Whoops, I misread before my coffee and thought they were talking about capitalism generally.
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One critique of capitalism for housing, is that private housing doesn't get built in a bust cycle, or generally when it's no longer profitable to do so. The recent boom can be traced back largely to supply not recovering to pre-2007 levels, and the market being unable to make up for lost time. https://fred.stlouisfed.org/series/HOUST
I am not aware of a housing market that is nearly all private that has built its way to affordability, short of massive economic collapse (e.g. '90s Japan) or some other catastrophic event.