Yes, an open policy for foreign students is good for the U.S. government, because it opens the United States up so that young people can meet Americans and see what our country is like. If they are not allowed to come see our country, they will never see that we are good people, and they will believe propaganda that says we are not.
Governments and universities competing to attract qualified students from around the world is a good thing. Of course the prospective student should be screened to make sure they are not affiliated with a terrorist group, but universities should definitely look for students all around the world that are exceptional. This will be good for the country the student is coming from and the country the student is going to as well.