I'm a bit skeptical that students are a big source of trouble. The vast majority come here, pay universities a lot of money, spend additional money in the local community, get their degrees, and then go home or maybe stay and work in generally high paying jobs, continuing to contribute to the local economy.

All that said, nobody has a "right" to come to the USA to study. It's something we allow, for a lot of good reasons, but there are doubtless a small number of people that we would not want here.