You know, I think that we wrap our children in too much cotton-wool sometimes. Obviously much would depend on the individual child in question (their age, maturity, and abilities), but I don't see any reason to blanket ban them from using any tools until they're a certain age. Except power tools, perhaps!
My eldest daughter is 13 years old (will be 14 in February) and I trust her completely around a stove and sharp kitchen knives. She can, and often does, make full dinners for the entire family, unsupervised. It's an incredible help because her father and I both have to work full-time, but I had started teaching her how to cook and how to respect the dangers long before I had to go back to work.
My next daughter is nine years old and has been using "dangerous" tools for some time. Two years ago she used a soldering gun to build her science fair project (supervised). I wouldn't allow her to use a sewing machine or a rotary cutter unsupervised, but if I was in the sewing room and she wanted to work on her projects, I would let her have at it.
My youngest will be 6 in December and she isn't allowed to use anything except pins and snub-nosed scissors (supervised of course!) As she gets older I'll "graduate" her to more things she can use.
It wasn't that long ago that children and teens/young adults were expected to know how to use and do things that nowadays we think they can't or shouldn't be allowed to do.