Capitalist free trade isn't purely the first point, especially around the reason for why people like Obama or Biden support it. State department spooks that advocate for free trade are much more nationalist than liberal.

There's much more of a real politik nation building side to it that has nothing to do with making corporations richer. The US saw that other nations could maybe someday outpace them because they had a larger population, and in turn would be able to out compete because of larger economies of scale for their corporations. Transnational megacorps were seen as the only way for the US to have any sort of economic growth (but really sustained position economically in the world) in a world where China or india became developed.

Also I tend to think liberals agree on the point about free movement of people, if anything they're more supportive of that than the left is.

Lastly, capitalist free trade is absolutely a good thing for the professional middle class. It means both higher salaries and cheaper goods. The only group that suffers from this in wealthy countries are people working in factories (resource extraction like coal mining/logging and farming also benefits from free trade).