PS The number of roles that there aren't qualified Americans for could be counted on one hand. This has always been about reducing salaries, not shortages.
Of course I am exaggerating, but this is not a 1 dimensional problem.
This is why in the modern world some sectors are always crying about "worker shortages" while asking always more migrant workers to come in - salaries are compressed as a result, and locals have no incentives to enter the branch.
Hence importing workers may be useful for needs that are limited in time and space (say, install a specialized foreign machinery in a power plant), but systematic importation leads to dequalification of the local workers, who flee the branch that has now low salaries.