No, see https://news.ycombinator.com/item?id=44866613. If the theory of comparative advantage is to give any useful advice, it cannot just rely on people doing "the right thing". That will quickly make it into an unfalsifiable tautology.

In this case, you also forget that the pricing signals have a time horizon, which is bounded by the expected time of survival of the private company being non-competitive. But government (society) can take a longer term view than a company that is influenced by pricing signals, See the LG example I gave elsewhere in this thread.

Another reason is incomplete information. Free market works in theory because you assume complete information; in the real world, this is not the case.