It is considered bad form and even technologically troublesome to close open connections at the gateway.
If you want central managment even from work, then create a shutdown script and have it shut down all the networked PCs, then manage the 1 cron job from your "server". If you don't already have it, set up RDP on your main PC to push the script. You will find this a much more manageable central spot for managment to boot. If you want to get fancy set up WoL scripts and blink the PCs every 5 minutes, this is particularly effective in a school lab.
While I certainly respect the argument that this is more force than necessary, if the only tool we have is a sledgehammer, we work on our finesse at cracking eggs with them. As is this is about the limit of the control we have with the tools on hand.
//Anything below is merely my incessant rambling and should be taken with less than a grain of salt. But I like hearing myself type, so I will continue.
I don't have any young ones (much to the glee of the female species as well as my parental units who don't consider me a prime candidate for spawning), but if I did, and the authority of my will was insufficient to ensure compliance then such measures would be a boon as they strongly reinforce the (possibly mystical depending on age) control you have.
Then again I was raised with 24/7 completely unrestricted net access from a young age (other than the school night lights out, which could be very literal), I more or less roamed free. I would also be extremely foolish not to think that my parentals were ignorant of my online mischief. My father has been in IT my entire life, thankfully the arms race stalemated peacefully when I became an adult (that and a format to my favorite Linux distro plus TOR can significantly cut my concerns, at that point physical monitoring is most likely).
That isn't possible if you have a child who plays WoW, WoW is much harder than any drug to kick. I lose friends to WoW more than any other drug.