There is a difference between the government-citizen surveillance and parent-child surveillance.
In both cases, a figure of authority (legitimate authority!) spys on you, pro[poradly for your own good. (Maybe even really for your own good! Just because the NSA's spying hasn't actually successfully foiled any terrorist plots yet doesn't mean that all spying programs of that sort are ineffectual...)
The one difference that I can see (and it's not an unimportant one) is that a good parent is open about what they are doing, and talks to the kid, gets the kids opinions. While organizations like the NSA try their hardest to make sure the citizenry don't even know that they're being spied on. This is a way in which a parent's spying might be not quite as bad.
However, remember that at least in theory the USA is a democracy, while a family is best described as a dictatorship. In the ideal world where the US government actually listened to its citizens and engaged in discourse with them, the USG would have by far the moral high ground over parents, even over parents who run a benevolent dictatorship where they actually listen the kid and make family policy accordingly, as a benevolent dictatorship still has certain problems when compared to a true democracy.
Surveillance has a chilling effect and parent-child surveillance is no different.
If I had to do this, I would have just avoided the internet as much as possible. I suspect most kids beyond age 9/10 are roughly the same.
I would never have learned to program, never have started reading HN, never have browsed Wikipedia except for specific queries. I would never have acquired the information or communication and technical skills I currently possess. I'd be a completely different and vastly inferior person looking at a much less interesting future.
> It doesn't have to lead to blocking and restriction
"Monitor and supervise" is orders of magnitude worse than content filtering. This approach forces children to block themselves from having any sort of individual experience. If your child is even slightly introverted and is old enough not to not want to share every second with you, "monitor and supervise internet activity" is equal to "learn about and engage with the world around you as little as possible." It sends a message that by default, information is bad - any time you do seek information, you know you'll have to justify your curiosity. This doesn't just apply to objectionable content, it applies to everything.
I was happy to show my parents my finished projects and even wrote a few specifically for family. If I were getting interrogated, incompetently, about every intermediate step ("Why did you install django-south? What's a database? What's a schema? What's a query? What's a function? Oh, is that like a ___? No, mom, go away.") I would have just watched mindless TV instead.
Could you imagine knowing that you will have to discuss every link you follow and every Google search you enter with anyone, let alone your parents? That's horrifying.