My kids are teenagers now, and survived their earlier youth under our parenting approach of including them in activities and hobbies pretty broadly. They've gardened, done landscaping and hardscaping, painted, sanded, worked with manual hand tools (hammers, screw drivers, miter saw), and been around my woodworking for about 10 years of their 13-14 years.
In retrospect, the most dangerous of any of those activities was probably the hardscaping - the kids tag teamed to move heavy bricks across our property and stack them. My son slightly pinched his fingers between two bricks when moving / stacking for us when he was about 8 years old... He had a nice short cry, iced the boo boo, and finished his chore with a new method on how to put the bricks in the stack without repeating the injury. The risk in this case felt appropriate and manageable to us, and he was proud of 'manning up' and finishing his task with a blood blister on his index finger.
As the years have progressed, the areas of risk we are willing to engage increases. Both of my kids have now completed multiple shop classes at their middle school, so beside my teachings, they're getting professionally taught too. As such, my kids are now permitted to use some specific tools (e.g. hammer, battery operated drill/driver) completely on their own (as long as I'm someplace within ear shot), and the drill press, miter saw, jig saw, and band saw with me standing next to them. These are tools they use routinely at school as well. They're still intimidated by the table saw, router, jointer, and planer, so the time's not right for those just yet.
The rules in our shop are so well communicated that neighbor kids know them. Ear protection, eye protection, proper footwear, don't touch anything ever unless I explicitly state that it is ok to do so at this exact moment. Etc.
All this to say... I agree with the OP that I think kids are capable of a lot. With firm ground rules, respect for those rules (and those setting them), careful supervision, and appropriate safety gear, they can really gain a lot by being part of a shop environment. My gut tells me that the OP is setting clear rules, carefully supervising, and that his kids are abiding by his requirements.
- Bob R.
Collegeville PA (30 minutes west of Philly)