Your (likely rhetorical) question presumes that a nation which is devoted to free markets would require housing to be distributed via free markets, but that's not necessarily true. In fact I'd say there's a lot of evidence built up now that the free market is in fact, not actually that great at distributing property, because necessarily to engage with a market, one must have money, and everyone needs a home, but not everyone has money.
Personally in my ideal world, we would distribute life's essentials in such a way as to be free at point of use, and then leave markets to handle things they're actually good at, like televisions and such.