Well, your students are probably texting so much in class, because they can't call the person they're texting with. Perhaps texting is the middle ground between leaving a voice message (which they won't do anyway) or calling (which would be totally inappropriate since they're in class). If they could, they would definitely call, but they can't, which is why they're texting instead.

I think it's all about relative advantages. What's similar between voice mail and texting is that you don't reach the person directly the way you do when you call him/her. The difference is that you don't have to call a number in order to check your messages, you just receive them directly on your phone. This, combined with the basically non-existent practice of using answering machines (I remember how confused my father was when we got a new phone that had an answering machine built in it -- the first thing he did was to switch it off) may be the answer to your question.