Neither you nor I is free to emigrate to the next hot ticket Third World low wage haven that will attract the capital of those who would otherwise pay us.
But it's not about emigration. I'm free to charge $5/hr and still live in America. The problem is that I'm used to a standard of living that requires me to charge $20/hr, and also I get services and goods from people who are used to having a high lifestyle as well. So, I might not have the same lifestyle here for $5/hr that I would have in India for $5/hr, but at least my new wage would be competitive.
Therefore, your argument doesn't hold water. It's not about "capital being portable but labor is not". It's about people charging a lot also being satisfied only with a higher standard of living.
It's like we're living on one side of a flood control dam, and the rest of the world is on the other side with a much lower water level. Sure, there's going to be an amazing change of water, and a lot of swirls and stuff while water is trying to seek its own level. And people may even drown in the middle. But when it all levels out, it'll work again, because it'll truly be a level playing field again. It'd be crazy to keep saying "no, that dam must remain in place". Not now that we've already let the crack open.
Nobody owes you a job. If you can't compete in the global market, you need to figure out what to do differently so that you can.