In a normal market place this might be true.
However real competition seems to be failing in huge areas.
So in practice just a few company's are running the markets.
This is partly due to enormous costs to get into markets and partly because things are simply not that easy to compare.
So how much choice do we have in reality?
Comparing health care insurance is not that simple for example.
Lots of people won't read all the insurance stuff and others will just not understand all the implications.

Not to say that all company's are bad...
Just that government at least seems to have the "do no evil part" (well, intentionally :) right

Lately the company's seem to cash-in in high tides while in the bad times the financial losses are put in the public domain.
A few examples to think of are the Banking & Car industries.

So for my part really important things, like healthcare, should be run by the government.