Yes torrent and file-sharing in most cases violates copyright and is therefore illegal.
That fact won't stop people, especially teens, from doing it. But it is a fact.
As with most things involving kids, open, healthy and honest communication is the best way. If you don't have that then no constraints will really contain them, they will find a way around them, they will sneak around behind your back, and you will lose their trust.
Edit - I'm curious, do you believe it's acceptable to spank children?
You're acting as if there aren't negative impacts to privacy. Adults should not have to give their identity over to web sites to enjoy content. Identification theft is a real thing.
Moreover, we already have solutions for this. Parents can block content at the router, and at this point every ISP allows you to set up security and content filters.
This is puritan, social conservative bullshit. It's a thin edge of the wedge ultimately aimed at making pornography illegal.
I'm curious - are you religious?