First, Ricardo's theory of comparative advantage assumes that capital is not mobile, whereas "free trade" globalization is in fact as much about free investment as about trade, and is very explicitly premised on capital being mobile. As soon as investment moves around the world, Ricardo's math falls apart. So for instance, if you have two countries, we'll call them "country crap" and "country awesome", and two products, A and B. If country crap is half as efficient at making product A, but 80% as efficient at making product B, compared to country awesome, under Ricardo country awesome should specialize in making product A and trade with country crap to get product B even though country crap is still not as good at making product B--because country crap still has a comparative advantage at product B. This holds as long as country crap has local investment funds that will stay in country crap and have to be invested in something. But, if investment can just flow from country crap to country awesome, the result is that all the investment should go to country awesome and country crap should make . . . nothing, and country crap's citizens should buy all their products from country awesome until they starve because they aren't making any money. The pursuit is not of comparative, but absolute, advantage.
Clearly from the point of view of the public good in country crap, this kind of free trade does not produce a lot of advantages. They would be better off erecting trade barriers to keep production at home, or at least investment barriers to block capital flight so that local capitalists would have to invest in local production. Not that the latter is easy to do . . .

Second, the basic idea behind comparative advantage, like much economics but particularly neoclassical, assumes a timeless present, or at least a country having eternally static characteristics. But generally, no country has an eternal comparative advantage or disadvantage at making manufactured (and other technological) goods. Stuff like that applies to bananas, which Hawaii is always going to be better at than Canada unless global warming really gets out of control. With manufactured goods, it is possible for countries to gain efficiency at doing it until they have an advantage against other countries they previously had a disadvantage against. However, gaining efficiency at manufacturing production is best accomplished through the co-ordinated use of protectionist measures. The United States immediately post-revolution successfully used a raft of protectionist measures to nurture local manufacture away from British competition. Ricardo's arguments about the superiority of free trade were in part a colonialist argument dedicated to blocking economic development in colonies. It is no accident that there were often much more explicit blockages on competition from colonies--many Caribbean colonies, for instance, were explicitly banned from producing most manufactured goods, from cloth to nails, so they would be forced to import them from the colonizing country. India had similar bans under the Raj.

Finally, all else being equal, with machinery, regulations, transportation, taxation et cetera all costing the same, investment will go to wherever wages are lowest if there are no barriers, because lower wages is higher profits. From the point of view of investment, this is an advantage, or higher "efficiency". In the long run it is possible to maintain higher wages than, say, Bangladesh's, only by trade barriers. And since the difference is all about higher percentages of the selling price going to profit, less to employees, the lower prices will never ultimately make up for the lower wages.