You choose median wellbeing as a “fair” judge of what trade policies are good or bad. I prefer to think from a military perspective. Large aggregate GDP (which free trade facilitates) promotes a stronger military as weapons may be purchased. Potential soldiers are more plentiful if I were to buy into your median income argument.
Larger aggregate GDP does nothing significant for the ordinary guy on the street if it is not adequately distributed such that the ordinary guy on the street can get a job that can provide for himself and his family.
A strong defense does nothing significant for a homeless guy with no way to feed his family, or a guy on a minimum wage while multinational fatcats rake in profits that wind up offshore.
Overweighing defense works out to a defense of a system of economic enslavement. Anyway a society consisting of well paid soldiers at the top of the economic pyramid is likely to be a dictatorship, because in order to feed your family, you need to be in the military or government, a la North Korea. What kind of society does the NK military have which is worth protecting? —a hollow society devoid of well-being for the median citizen.