Not only is healthcare not working under private administration, the Republican truism that private industry can always run things more cheaply and efficiently than the federal government has been repeatedly shown to be a blatant lie. In addition, there are public-interest functions that are anathema to the corporate mentality, the ostensible role of the FDA being one obvious example.

Unfortunately, the corporate theft and takeover of the government, which had its beginnings with Reagan, has corrupted the FDA in a variety of ways:
A huge variety of alternative medicines, some effective and many worthy of Dr. McGillicuddy, have been permitted onto the marketplace with the caveat emptor “These statements have not been [and, due to lack of corporate interest, will not be] evaluated by the Food and Drug Administration [whose loyalty belongs to the pharmaceutical industry]. This product is not intended to diagnose, treat, cure or prevent any disease [because, as a genetically unmodified natural product, it is not patentable and therefore does not serve the interests of the FDA's constituents, the American corporate culture].”
Unconstitutional establishment considerations prevent the FDA from ruling favorably on abortifacients.
Political/financial (read “bribery”) pressure from the likes of Monsanto prevent the FDA from endorsing the labeling of foods as derived from genetically modified seed stock or, for example, harvested from animals treated with questionable drugs for questionable purposes or, similarly, fed questionable feedstocks for unquestionably and irresponsibly cheap (as opposed to economical or inexpensive) motivations.

In short, hte government’s rightful business, which it routinely shirks under insidious conservative administrations, includes every necessity that is anathema to the pursuit of profit at all cost. It is why we pay taxes, and because corporations in pursuit of said profits without principle necessitate such oversight, it is why they used to pay taxes.