The fencing around schools is a result of two factors -- the first to control the environment (no guns, drugs, or pedophiles since you have to go through the school to reach the play area), and the second a result of a study that found little kids would play all over a fenced area, but if the fences were removed, they huddled anxiously in the center, unsure of how far they could go.
The key points to that, I think, are the study was about LITTLE kids. Like, kindergarten age. And that they had previously gotten accustomed to a fence, which was then removed. Older kids, or ones not accustomed to fences, would of course have different reactions. But the lesson taken by school boards around the country was "kids need fences".