Prosperity has everything to do with it. If the government can really do everything more efficiently than can the private sector, then the most prosperous countries would be those where the government does the most. Do you really think that North Koreans are innately less industrious and/or less intelligent than South Koreans? (Well, except where North Korea's collectivist policies have resulted in stunting and malnutrition.)
There is absolutely no big chunk of tax money being wasted. The OP's article states that private prison corporations provide little or no savings; it did NOT state that private prison corporations cost more money. For the record I'm against private prison corporations - I find that disturbingly close to slavery or at least indentured servitude - but I have a BIG problem with this war on profit by the young and the stupid. The profit motive (enlightened self interest) is what made this country and, indeed, the West so successful, and the further we move away from it the more we will approach North Korea and Cuba.