Would those things be better if they were privately run for profit? My personal opinion is that there are certain things that you can't allow the the private sector to run because it leaves too much room for abuse by individuals looking to make a profit. As a Canadian who's mother is a doctor, the one thing that really bothers me about the healthcare system in the US is that from a business stand point insurance companies are more profitable the more claims they deny, which really doesn't sit well with me. I'm not saying our system is perfect by any means, or that the US doesn't have a high quality of healthcare (if you can afford it). But the thought of someone making a profit on someone else not get a medical treatment that they need leaves a bad taste in my mouth.
Libraries, police, roads, and the army are great examples in favor of government. All you've done is demonstrate that there are exceptions, as there are to anything.
I always wondered if we could run a 'medical service' that was a viable 'public service' alternative to spending time in the military or peace corps. Basically let young people volunteer to be health care workers, give them training, and guaranteed employment for 4 - 6 years. At the end of their enlistment they can go out to the private health care system or other jobs.
Can you imagine the horror of spend a billion dollars a week "invading" a country like Afghanistan and having a 100,000 health care workers on the ground making everyone healthier?