Immigrants completing PhDs in the US and then staying on to become residents is one of the things that has given the US a lead in technology.
Spending US money to train PhDs and then telling them to "get the hell out of the country, you're not welcome here" is the US shooting itself in the foot.
It took me 6 years to complete my PhD in the US. Would the border guards have let me back in to complete it after the new 4 year deadline? Who knows.
For more than a dozen years after I left the US, I always told European academics that they should definitely plan to work or study in the US at some point. Now I tell them they should live and work in another country than the one they were first educated in, but I wouldn't go to the US if I was them.