is it cheap and fast because they are run efficiently? or because they are subsidized by taxpayers or they are not burdened by the same rules that potential competitors have to hoop through?

Having worked for a small gov't agency in NYC and personally witnessed all sorts of waste and incompetence, I'm a bit skeptical that this is at all possible. I don't think efficiency or cost-effectiveness is not something that comes to my mind when someone talks about gov't services.