In my own case, when I was 14, my parents installed a parental firefox add-on. I disabled it using safe mode in one day. They found out through a keylogger they had on my computer(which I removed, ofc), and they proceeded to install a near-impossible to break secure control. Can't remember what it was called, but I struggled with it using proxies for a few months, and then I figured out how to remove it by deleting from the registry. Since then I've had no trouble.
The moral of the story is not to try.
Reminds me of the time my Mum put a boot password on the family PC, which lived in the dining room. I read all sorts of things when I'm bored, like motherboard manuals...so, it took me all of 5 minutes to bypass that as I'd previously read about it. This was back on Win 95 or 98.
She got most of her 'advice' from her work's tech support, but as I'm also qualified to work in that area it was a complete waste of time.
When I was 16 I had my PC in my room. (To this day, still do). I bought it myself. It was never an issue of removing it. I've had all sorts of consoles and PC's since I was about 5. The only time a bit of an issue came up was when we got the internet. I had the phone cord running from my room to the lounge room and it was back in the day of no broadband and splitters. You go online and no one can ring in or out. I got in trouble a few times for 'tying up' the phone lines. It was expensive back then, too. Mobile phones weren't as common, plus expensive as well.
In this day and age if I had a 16 year old I'd let them. I had one when I was that age (and before that). It'd be fine by me