I feel like there are some particular cultural attributes in the United States that make this useless at this point.
The United States has a very individualistic attitude. Sure, we can pause travel from Europe, but the current administration is very anti-europe. Can we pause travel in the US? I strongly doubt that we can effectively given the strong anti-expertise attitudes as well.
My guess is that the United States will become a more major hot spot for the virus than other locales. It will spread rapidly and the supply hoarding and sad state of our medical system will mean that in a few months, other nations will be rejecting flights from the US.
It's a prediction, a guess, but there are aspects of our culture that just makes it seem very likely. I'm not going to make any more predictions than the idea that we'll have more cases per capita than any other developed nation.
It's be interesting when I'm proven incorrect over time.