Periods of time spent in other cultures would help any student foster a greater understanding of said culture and a renewed appreciation of the student's own culture of origin. What is more it would be a much more effective method at teaching students a second language, something that native English language speakers fall especially short on. Furthermore, the benefits would be bidirectional, the student’s presence also likely to foster some form of cultural exchange for the natives of the country they are staying in.
While the positive sides are various and indeed obvious, the main downside would be the massive expense in sending so many students on exchange programs. However, if you take the United States alone as an example, with a military budget of $696 billion in 2018, surely money could go into schemes to actually foster better international relations rather than further destroy the United States’ image abroad? Although some may argue that US military spending is somewhat justified, with departments of the military such as the pentagon making catastrophic accounting errors in recent years, money could possibly be stripped from departments that cannot account for it when audited, and put into more positive proposals.