Why is that? Don't you like to watchful for physical injuries? Then, why not emotional and age-related mental injuries caused due to unsound exposure to say adult content?
With today's technology you could also simply require your child to maintain an ongoing speakerphone call with you the entire time they are at school, so you can monitor emotional and age-related mental injuries caused due to unsound exposure to bullies and other students who have unrestricted internet access. That seems intrusive, just like active web traffic censorship.
For what it's worth OP, my parents' own netnanny experiment was what introduced me to the magic of Ubuntu Live CDs and from there, Linux and programming. So maybe circumventing parental controls can be a valuable learning exercise for the motivated student.