Is it really that hard to believe that the US enjoys a disproportionate number of smart immigrants that isn't sustainable with the US's population alone, and that we are at risk of losing this extremely valuable population? To believe keeping out immigrants won't harm the competitiveness of American talent means you believe that the natives are some how exceptional compared to the rest of the worlds population by place of birth alone. Or do you just not care if smart people live, work and defend another nation if it means people who got here first have higher employment?
The overwhelming majority of us would be pleased if smart people did their work anywhere they find accommodating. Why should it have to be in the USA? Science and tech innovations are quickly shared around the world in the present day.
And the present system means that Americans are almost entirely blocked from pursuing careers in science by the awful economic prospects. Foreigners that come here can always get good appointments back home that will support a family if they can't get tenured in the USA. Americans would be out of work with zero savings and mediocre prospects at 40.
If you think Americans have something valuable to contribute to the world of science beyond than our cash support, then you can't support the level of mass foreign migration into science schools and professions.
I mean, sure, I want them to be able to work anywhere, but as American citizens we are enriched when they work in our schools, our private companies, in our government and especially in our military. I also don't believe that they are any less deserving than Americans at those jobs, or that Americans have any birthright to them.
Why don't Americans, discouraged by the economic prospects of our careers here go to foreign nations and support a family? Foreigners are willing to uproot themselves to start in the United States. And we are all better for it.
To answer your question, they do. I got a physics PhD in the United States. After being disappointed by the poor prospects offered the, I moved to the UK, where I now hold a prestigious permanent position. No more post-doc hopping for me!