An interesting point on healthcare: can you name the major turning point from the days of old when doctors made house calls to today? It is the establishment of Medicare and Medicaid, which permanently distorted the entire health care market. The government is very much involved with our health care system, and the result is growing trouble in health care. Adding more regulation will make it worse - history makes this point quite clearly.
I think government should provide our National Defense, the Justice System, and Police.
I would guess it was due to the previous difficulty of transferring injured people when today it is easily done with ambulance/automobile/helicoptor. Also, back then I imagine people would be far more reluctant to see a doctor so the serious cases only that would possibly prevent people from going in.
Plus, a doctor can't do X-Rays at your house or use his fancy gear.
I think government should provide our National Defense, the Justice System, and Police.