I do believe that it is useful and important to have internet access at school, but it should be restricted so then students can't search or do inappropriate things online.
So the first reason why I think this is because the internet is a great place to find information, especially recent information like breakthroughs in news. This is useful so then kids can not only be accurate on information in research, but also up to date. This will involve and expose students to real life situations and how what they are studying can apply to the world right outside of the classroom. You may argue that students don't need to research at school and can just do it at home. But that isn't necessarily true, because some kids don't have internet at their house and can only access it at school. In addition, when at school, teachers can help guide their students in research and with limited access to certain sites (especially gaming sites and social networking), students are more likely to stay focused when they research at school.
Second reason why I think that internet is important is so then students can send papers, homework, etc. To themselves for backup and to their teachers to turn them in right there at school. Many teachers now (or at least at my school) prefer that you submit things to them electronically and they put up assignments online. It's easy, fast, and saves a lot of paper. That's why if students wish to do their schoolwork in study hall or a free period, they are able to access the assignments online to do them or are able to turn them in right away once they are finished.
Lastly, internet at school can be helpful as learning materials. Many teachers often use the internet to search up videos, print out articles, and so on and so forth for students to enrich their studies. This, like the first reason, is for students to keep in touch with the real world. The difference between this case and the first one is that this will help involve the entire class while the first one is for individual enrichment. Involving the entire class on an issue is a great way to start discussions and debates that would often reveal the different views of others that are present in the real world. This will not only teach kids of different opinions, but also how to respect and tolerate them, both useful skills to have as an adult (although I am disappointed to say that not all adults have these).
Essentially, having internet at school makes things easier. It helps teachers with their job and students with their learning. Although I believe that the key is limited or restricted access. With these types of boundaries, it's good practice for students to stay on task and realize that the internet can also be used for useful and educational purposes.