I'd leave them for short stretches- nipping to the shop type- once they were 8 or 9, as long as they were happy with it. By 11 I was leaving ds for maybe a couple of hours. Now that he is 13 I have been known to leave him for the day- and I'm quite happy for him to cook while I'm away.
I know from observations made at other times that he will cope calmly and sensibly with any emergency. When he accidentally tried to boil milk in the kettle aged 9 (foreign family, not enough kettle experience
), he smelled the milk burning and very sensibly switched the electricity off and unplugged the electrics before going to tell an adult. He knows where the stopcock and the fusebox are. As an adult I have no specialist knowledge about these things that he doesn't have, and I know from experience that he is no more likely to panic than I am.
But if at all possible I've given him a choice.
Neither of mine has ever seemed particularly silly beyond the toddler years, nor do I remember getting into much trouble myself as a youngster.
I used to be allowed to take a boat out alone from age 11 or so and never misused the privilege: I knew as much about the signs of changing weather as the adults in the family did and was just as careful about mooring. I was allowed to bake and cook at home from an early age- and again I don't remember panicking if things went wrong: I expected to sort myself out and I did.
With hindsight (and experience from own childrearing) this clearly wasn't a one-off decision from my parents that now she is going to be responsible: it was the result of years of training, of years of being involved in the practical everyday life of the family and being expected to make sensible decisions.
But the decision thing works both ways: I would have allowed my children to come with me if they wanted to, and I am pretty sure my parents would have too. I think these things work best when you are following the natural flow of your child's development- at least up until a certain age: if they are nearing secondary school age and still unable to walk to the lamp post without you, you might want to put in some special training.