If somebody has to take the hit for corporations shutting down US operations and moving to third world countries it ought to be "Big Labor". Private corporations have only one primary function, to make as much money as possible for their stockholders while obeying the laws of their homeland. It is nowhere near their primary function to make union members wealthy beyond their dreams of avarice.
Of course nothing stops a union from from "passing the hat" among it's members and forming an "employee owned start-up" to compete with their former "Robber Baron" bosses either. True, it's never happened that I know of, but it is an option none the less.
In most manufacturing industries, the impact of regulations is greater than the cost differential of labor.