There are loads of examples of public services that might be more efficiently run with competition. Think about the US Postal Service. With the rise of UPS and FEDex, the USPS has had to improve and change to stay competitive. I think there needs to be a line drawn where there needs to be significant oversight because the services could have a significant impact on people's livelihood. Think about police or military, I am not sure that I want a private firm handling those sensitive issues.
