But the person who owns the property has every right to ask people not to trespass. How can it be a power play? I don't want people wandering into my backyard just because it looks intriguing, and I want to be just as respectful of other people's property rights.
I realize that most children don't think that way, and that even I, as a child, would have stayed out more from fear of the consequences than on principle. It wasn't until I was a teenager that I began to think about property rights. Before that I would have just thought the person who put up the sign was being mean. (And if they were that mean I didn't want to get on their bad side!)
But now I know that if children get hurt on your property, at least in this country their parents can sue you, even with the No Trespassing sign, if it is decided that the pond that a child drowned in or whatever it was that hurt them was inevitably too appealing to children. It's called an attractive nuisance. Since landowners might not be certain they know everything that could be considered by a court to be an attractive nuisance once someone was hurt, it would obviously make sense to try to discourage them from setting foot on the property to begin with.