I don't think that classical economists would make the argument that the market never gets things wrong, but they may have a different take as to why mistakes get repeated/aggregated and what to do about them. In the subprime mortgage example given, classical economists would point to three market problems - information asymmetry, agency problems and government intervention. Information asymmetry shows up when investors buy mortgage pools, but have no idea about the underlying credit-worthiness of the borrowers. Agency problems arise when the mortgage broker offering the mortgage has no downside exposure to default. Government intervention makes it all possible when Fannie and Freddie implicitly back the debt with the taxpayer's future income streams.
Anti-market types will search for solutions in more regulation. Market disciples would call for a break-up of Fannie and Freddie and increased information availability regarding the mortgages in the pools. We had plenty of regulations and regulators on the job already, and they couldn't get past Barney Frank and his gang. So going forward, this market disciple would prefer we go with the approach of increased information and less government involvement. Of course, we are getting exactly the opposite.
How about both more information and more government involvement? See, who is going to make sure that the information provided by the private market is correct and sufficiently adequate -- the market? Oh yeah, that may be, if we trusted those who made the market, but in the case of the mortgage industry, it's painfully obvious that information is filtered and tailored to the needs of the shareholders of the company with the mortgage product. Unless the level of information dissemination is managed by the government, there is nothing to ensure it gets done. Of course, the government can and does frequently do it wrong and do it badly, but I'd rather have that than a private enterprise with no accountability and the arrogance of the profit motive determining how much information is enough information.
Another fallacy is the idea that Fannie Mae and Freddie Mac can suddenly be jettisoned in favor of a less government-reliant substitute. When one considers the facts that Fannie and Freddie literally have trillions of dollars at their beck and call, and own trillions of dollars' worth of mortgages, which are then sold to investors around the world, which gives it and us more money to lend out, which keeps more people employed (like me), I can't see a private market alternative that wouldn't take years and years to develop.
Finally, the reader gets it partially wrong that brokers have no downside to default. It is true that a small shop that does nothing but broker loans has little downside if a loan goes into default, since by the time the borrower goes into default that broker may be out of business or may be forced out of business. Still, there are those shops who use their own funds to make loans that they can sell directly to Fannie/Freddie or an institutional lender who then turns around and sells it to Fannie/Freddie. If a loan goes into default within a certain period of time (usually 90 days), those lenders must re-purchase the loan. There are also financial checks on the sellers of those mortgages to make sure that they have adequate loan loss reserves to be able to repurchase the loans. True, those shops could also fold up and declare bankruptcy, which basically proves one true thing: the locked door only keeps out the honest man.