I think the unfortunate truth is that US academia job market is already highly saturated.

Look, a professor may need 5 to 10 PhD students, but there won't be so many positions open when those students graduate. In the past physics and biology graduates will try to stay as postdoc or research assistant as long as possible. Or find a position in industry. Nevertheless, this is just not a sustainable model in the long run. Eventually it will come to a point where more and more of them will go back to their home country.