Maybe I'm old fashioned, but at one time it was believed that there was a foreign policy angle: The people who come here end up liking our country and bringing that good will back home with them. They also learn the reality of what it's like here, which is often contrary to the propaganda that they've received at home.

They also spread the prestige of Harvard. If Harvard were to adopt US-only admissions, their reputation would go down, and the degree would be less valuable for the remaining American students.