It is undisputable that the greatest danger of child abuse comes from people the child knows and trusts — their father first of all, but also close relatives or authority figures. Although abduction and abuse by a stranger is a horrible tragedy, it happens very rarely. Thus it seems clear to me that efforts to target pedophile strangers — such as sex offender registries, or the more recent program in New York City whereby you can be ticketed if you’re near a playground unaccompanied by a child — are disproportionate.
Even worse, however, they put the child at even more danger of family abuse, as it has the effect of turning the family unit into a kind of fortress. Indeed, apart from the constant brainwashing to make sure children don’t talk to strangers, it seems to me that some adults may even try to avoid any direct interaction with children they don’t know, so as to avoid accusations of pedophilia.
Even if they’re not trying to escape abuse, children would definitely stand to benefit from more interaction with people who don’t believe (consciously or unconsciously) that they own them and don’t project all their hopes and dreams onto them. Cutting them off from all outside, unfiltered influences means treating them essentially as the property of their parents — as Justice Clarence Thomas apparently believes they should be.
We often tend to talk about the negative effects of overparenting on people’s adult lives, but this misses the point in two ways. First, it overstates the impact of parenting — in reality, children are separate people and are normally able to more or less get past whatever “issues” arose from their upbringing without any major problems. (Here I’m drawing on the Last Psychiatrist post I linked on the sidebar.) It sometimes takes a long time, but (outside exceptional circumstances) if you’re still shadow-boxing with your parents at age 30, there’s something wrong with how you’ve chosen to live your life that goes way beyond anything your parents have done.
Second, and perhaps more important, it ignores the fact that living in the pressure-cooker of an isolated nuclear family is no way to live for the child when they’re children. Even if they get over it when they grow up, it is still the case that living under constant surveillance (justified, in good totalitarian fashion, by profound love…) and being cut off from any meaningful contact with the outside world is miserable.
An und für sich 
Arguably there’s a similar dynamic at work with the excessive paranoia about women being raped by random strangers on the street. Again, it’s horrible when it happens, but it’s very rare compared to rape by intimate partners or other trusted people — I’ve even seen statistics indicating that women walking around alone are less likely to be victims of crimes than men walking around alone. The effect of making women afraid to go out by themselves is similar, too, making them more dependent on the men in their lives, etc.
It sounds good in theory but is impossible in practice. I think you do not have children. They do spend a significant amount of time at school, for example. They go to classes and so forth. Contact with actual strangers would do nothing to protect them from their parents. Leaving them free to talk to a random person in the park does not enable them to speak out about anything they experience at the hands of those with actual authority over them.
The ‘don’t talk to strangers’ motif was also fairly common when children really did have the ability to run free. It was a way to enable them to run free. The idea was that children would figure out that there were some people who did pose a possible threat but otherwise they could be out and about alone or with their friends until dinnertime.
I also think you have not been abused. I spent a huge amount of time running freely around the neighborhood and was often cared for by adults who weren’t my parents–you could even call this co-parenting–and I did not tell anyone about the abuse I experienced. As long as parents rule the child and are the authority, the child is likely not going to feel free to bring in others. In fact, for many children it would be very stupid to do that. From a child’s perspective, adults tend to stick together and telling anyone anything is a huge risk. It’s hard to get around this unless you loosened the bond between parent and child significantly and changed children’s views on adults–and those two features of childhood are not really that recent.
Second, I do not know what you mean by ‘excessive paranoia’ surrounding rape. Whose paranoia is this? You seem to be either saying (a) women need to be braver about the threat to them or (b) some other entity (the media? the culture at large?) is fomenting paranoia and women are somehow helpless with respect to it. At least some theorists have argued that rape is a type of terrorism. So the intention of some rapists is to terrify women–and they succeed. But it’s hard to know who to blame for this. In any case, it’s not so simple as aligning one’s views about one’s safety to statistics about actual risks. If it were, terrorism would never work. The fact it does work shows that we have difficulty controlling all our emotions when we do face certain kinds of existential threats, even small ones.
This whole post may have been ill-considered.