I clearly remember being 6 years old and out in the woods with my brother, who was 4 or 5 (this was in Korea) and coming across an electricity sub-station with the gate unlocked and open. My brother wanted to go in and play; I didn't let him. I was sensible enough to know it was dangerous. We used to catch buses into town to buy sweets. To be fair, we were supposed to walk, not catch the bus as my mum worried we'd get on the wrong one and end up in the next town over. But we did it anyway, got there and back.
When I was 8 and my DB was 6 we were running feral. This was in South Africa (I get around a lot), supposedly we were being looked after by the domestic help while our parents were at work, but all the neighbourhood kids just did what we liked - went out, walked for miles, played in empty lots. We showed up at home before our parents got in.
I leave DD1 (6yo) alone for 5-10 mins here and there. I tell her not to open the door and leave her with the phone set on speed dial to call me if she needs me. I think she worries about it more than I do. She's very sensible and has never shown the slightest inclination to light the hob or play with matches.
How on earth do you teach your children independence if you never give them any? Children used to be considered adults at 11 or 13. I can't believe some of you wouldn't trust children as old as 10 to be left alone - why are you not teaching them to look after themselves?
It's all very well to say that something might happen. But if you give your children responsibility and put them in mildly risky situations, they learn how to deal with risk and solve problems. If you wrap them in cotton wool and never let them do anything on their own, how will they grow into free-thinking independent adults?