The problem if they are privatized is that nobody will be regulating them at all. But I guess that risk factor will be incorporated into their stock prices.
Their market share is steadily declining. The large banks are now issuing securities and are actually behind the effort in Congress to restrict Fannie and Freddie from owning securities.
How about the SEC, they regulate all public companies.
As a mortgage loan officer, I have fewer and fewer loans that I do that end up being Fannie or Freddie loans.