No, the school computers and Laptops should not allow unrestricted access to the internet due to cases of cyberbullying and inappropriate websites and they would not be able to get on with their work as they would be on social media. The internet should be restricted so that only internet research can be accessed. However restricted or unstricted internet may not have any impact on cyberbullying. Student Blackboard internet/e-learning should be allowed but not any forums or interactions from other students or be closely moderated. But the unrestricted access to the internet at school could catch the cyberbully and who it is if they are known to the victim and so because it would in school hours on a computer the school could do something about it so that is is not just a matter for the police or for the parents to deal with.
Maybe the schools could experiment with both restricted and unstricted to see what is best.