Capital gets to traverse the world - its factories spewing waste and arbitraging cost of living and currency differences in SE Asia, its profits reported in tax-resorts like Ireland and the Cayman Islands, and its protection guaranteed via the US Military courtesy of the US middle class.
But should a lowly citizen try to pull a stunt like importing a medicine from India or purchasing a text book from Hong Kong, well that's against the law.
Global free trade without global freedom of movement is just profit rearranging for corporations.
Even with global free movement people would not be able to do the same. I cannot live in California, build my house using Chinese labor prices, and be taxed as if I lived in Nevada.
You have to toggle both knobs at the same time to make sure the system doesn't become unbalanced.
With trade+immigration, you can't allow the free movement of capital without also giving people the option of following their jobs to places long removed from their origins.
Is it practical? Not entirely, but the road has to flow both ways.
If you wanted to balance things, you'd pair an open market with shared rules on safety, environment, labor rights, etc.
The ole' america swircherroo.
As an aside, you don't even have to have large migration to produce a new equilibrium. As long as workers could feasibly migrate, they can negotiate for higher wages in their home country using that as a BATNA.
Americans are not migrating to third-world countries because there are more jobs. That's not going to happen.
But no, Americans are not emigrating in bulk any time soon. The thrust of my argument today is simply that greater inflows to the US is part of the 'free flow of labor' equation.