Can you provide any arguments (or, even better, empirical evidence) as to why the government has more waste, incompetence and corruption than the private sector?
I'm not arguing one is better than the other. Just that both system are run by humans so I wouldn't say you'd have less corruption or waste in one or the other.
Provide me with an example of a fully functioning free market completely devoid if any government regulation or involvement?
If one doesn't exist, I wouldn't like our system to move into that direction based upon wild speculation and pure theory. The implicit assumption in free market models is that people are rational agents, when all research shows that people are highly irrational.
Wouldn't you like see evidence of how a free market would function on the scale of the United States? Like a scientist, not like a religious zealot?
In a "freely competitive market" (to use Adam Smith's original phrase) you can. In a market without that competition you can't. Sadly many markets in practice don't have free competition.