Well, the keyword here is "responsible parenting". The child has to understand that the restrictions come from you, and not from the computer. This means watching the screen together, and not relying on a fallible automated system.
Breaking SSL is not the answer for one more reason: with more and more web apps (cannot say "websites") relying on JavaScript-only content delivery, long polling, websockets, server-sent events, and who knows what else, there are less and less standards. Earlier, such nanny software worked because everything was text and HTML, and it is known how to stop bad things in these content types. Nowadays, we can't just block replies, because we have to substitute some dummy JSON (or whatever) instead, so that the app doesn't crash or hang - and such dummy replacement of the blocked content is application-specific.
Also, think about today's children, they are tomorrow's politicians: now you deploy an automated system that breaks the internet for them, tomorrow they will deploy an automated system that will deny access for you to anything published by the opposition.
Breaking SSL is not the answer for one more reason: with more and more web apps (cannot say "websites") relying on JavaScript-only content delivery, long polling, websockets, server-sent events, and who knows what else, there are less and less standards. Earlier, such nanny software worked because everything was text and HTML, and it is known how to stop bad things in these content types. Nowadays, we can't just block replies, because we have to substitute some dummy JSON (or whatever) instead, so that the app doesn't crash or hang - and such dummy replacement of the blocked content is application-specific.
Also, think about today's children, they are tomorrow's politicians: now you deploy an automated system that breaks the internet for them, tomorrow they will deploy an automated system that will deny access for you to anything published by the opposition.