The theory of free trade is that reducing trade barriers benefits everyone in the long run. But as has often been noted in these forums, free trade has only benefited US corporations. US wages are stagnant while corporate profits are at record highs.
What is the reason and what should be done, if anything?
Low wages are not necessarily a reason to change anything in the operation of markets. The immediate reason broader prosperity is being delayed is wage competition: Chinese and Indians now compete for jobs Americans used to do. Technology has prevented some deterioration by making American workers more productive per capita -- but at a cost of again shrinking the job market. High unemployment also puts downward pressure on wages.
The question is, is there anything wrong with the increased wage competition Americans are facing? Here I believe the answer is that foreign governments continue to intervene in market operations to benefit their own citizens -- and to the extent that they do that, American workers are facing unfair competition.
Foreign government protect themselves against American competition with a whole raft of measures, from subsidies to manipulating their currency, to outright trade barriers. The US can and does respond in kind to some of these unfair trade practices. But there is one large aspect that is not being addressed: there has been a huge influx of foreigners coming into the US to get jobs, but the number of opportunities for US workers to take jobs overseas is nowhere near the same. Again, much of the reason boils down to the US being a more hospitable environment for immigrants than vice-versa. Other reasons include that whereas many foreigners learn English, few Americans learn Mandarin, for instance. Chinese is not taught in American schools, by and large,
Trade should be free and fair -- and that includes the movement of labor. To the extent that trade is not free or labor cannot or does not move, the free market has been interfered with. In that situation, since foreign government are unlikely to stop, there is an an appropriate role for US government to step in and balance the situation -- with tariffs or with immigration restrictions. This should continue until such time as foreign governments adopt equally non-restrictive policies regarding trade and movement of labor.
India doesn't allow the US to send over Walmart employees to open up stores on every corner in India. There is massive political pressure to keep Walmart OUT of India because of mon and pop shops. Yet Indians come to the US in droves to work at high-paying programming jobs.
So people like to say "free markets don't work" or "there is something wrong with capitalism" when in fact the only thing wrong is a worst case regarding government intervention: best is no intervention, second best is equal (e.g. retaliatory), worst is unequal.
You don't want to be living in the country that is pursuing "free trade" when no one else is. That's a government failure.