There's a difference between goofing off or wandering off-task, and watching something that is wholly inappropriate in the classroom (sex/violence/language/etc).
For example, if you're supposed to be working on a science lab and you're watching some YouTube science experiment video, you should get back to what you're supposed to be doing, but it's not like you're watching a video that's Not Safe For School.
Another example would be if you're supposed to be working on homework during study time, but you're reading a Harry Potter book. To call something like Harry Potter or the Narnia books "Not Safe For School" is to expand the term past the point of any useful meaning.
Not sure why being labelled as NSFW/NSFS refers to sexual content only. I was of the opinion that your work computers are monitored, so anything you do on them that is not work related can cost you your job, sexual content or not.
By the same token of reasoning, kids going onto sites unrelated to school while they are in class can and should get in trouble.