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Others have pointed out that both the fire service and policing used to be run by for-profit companies. The military were the same back in that bastion of socialism - Europe.
It is now accepted that these things are the responsibility of a government to carryout on behalf of their citizens. Why should health care be any different?
There are 100's of reasons why cure rates for certain cancers might or might not be better in one country or the next. But as has been pointed out elsewhere infant mortality rates (often used as a proxy for poverty) in the US are higher than in any other Western country.
The US is the only 'civilized' country in which it seems to be perfectly acceptable for a boy to die from a toothache....
http://www.washingtonpost.com/wp-dyn/content/article/2007/02/27/AR2007022702116.html