What's the point of visiting students?
The main goal, from my experience, is the facetime with many different people. Skype is nice, but it's primarily intended for conversations with very few people. A visit allows students to to talk to many professors and students face-to-face in a short timespan, get to know the place, interact with students in a lab, and get a sense for what the place is like, something which is impossible over the 'net.

Also, this gives the university a good chance to see what the student is like. It's easy to look good on paper and can put on a clean shirt (pants optional) for a skype interview. It's a lot harder to keep up a fake act in front of dozens of faculty and students over a one-or-two day period.