I was on the radio the other day, discussing the future of Fannie and Freddie, when another guest said that all we had to do was fully privatize the mortgage market for all to be well. I know that I can't expect everyone to be aware of the 1920s, but the period 2002-2006 was a period in which the "pure" private sector took away substantial market share from Freddie-Fannie, and look how well that turned out.
Of course in the end there is no such thing as a pure private market, because when large financial institutions get in trouble, the government comes to the rescue, either through an injection of funds or through extremely low interest rates. We are all GSEs.