We have to give them a bit of space. I think I was eight and my sister was 4 when my mum used to let me take her up to the park (this was 40 years ago) and she was happy to do that because the park was on the same side of the road that our house was, and that at the entrance area of the park was someone she knew. As it turns out, the woman my mum knew was of no use whatsoever on the day I needed her. However, 99% of my experiences in that park were based on freedom and "Blimey the moon looks big, I better go back home."
My kids? Live opposite a park on a not very busy but occasionally mental suburban road. Some folks love to speed along our road for no reason at all (to my mind anyway, to them it's a place they can speed up and show off). I occasionally let my kids both go over to the park (oldest is 10 and youngest is 6) and then follow them and see what's going on if they're not back in about 30 minutes. They have instructions that they should come back if they feel unhappy, uncomfortable or bored. And sometimes a friend will call for the older one and I let her go over with her friend - they're often back before I think, "I should go over and have a look..."
Most of the children my kids come into contact with have elements about them that I'd not like my kids to have but in all honesty they need to develop (a bit of quick thinking, being properly streetwise, character judgement will serve them better than following my rules to the letter etc.....). You don't get that latter stuff unless you're able to push it a little as the child who needs to grow.
Damn hard as the parent though. Although to be fair to myself I learned most things on school holidays when I was supposed to toe-the-line and didn't.
When it comes to saying, "Go on then, come back in xx minutes," you have to have a bit of trust and a bit of optimism. Anything after that is hard work and good luck to us all if we want to bring up well rounded and savvy children.