Personally I do not wear a bike helmet, however, if some of my former mountain bike friends called up and took me out riding all day on trails I did not know then I would find a helmet and make sure it was properly fitted to my head. So I am not absolutist when it comes to helmets.
As it happens I have sold thousands of helmets and fitted a few hundred for people. Along the way I read the instructions and you do need helmets to fit properly, i.e. with the straps tight. I have also noticed that most cyclists including those in the peleton ride along with the straps somewhat less tight than they should be. Hence I suggest that rather than have helmet debates with people you helpfully point out to them that (if they are wearing a helmet) that the straps are dangerously done up. Point out to them that they could get strangled by their helmet in an accident if, due to the straps not being very tight, the helmet slips back. Assist them in getting their helmet setup properly, by which time they should not be able to move their jaw and give you any more lip :-)
Banning kids from riding bikes around cars? I can understand why that's considered a bit too overprotective, but helmets to me seem like a common-sense method of resolving a significant risk with insignificant inconvenience.
Other than that - let 'em at it!
From training wheels to full-speed downhill riding should only take 6 months. You want to encourage helmet wearing as a habit before that progression occurs.
My child had a very large crash that occured because he went down a hill and got confused as to which side of the bike the brake was on, because he was riding an unfamiliar bike. He had ridden down that hill many times. He crashed heavily at a high speed, enough to knock a tooth out and lost a lot of skin on his face, elbows, hands and knees. The helmet had serious damage and had to be thrown away. I don't want to think what would have happened had there been no helmet. He was 4 at the time.
I let them ride down hills to get used to the speed as part of learning, so that when they do get older they don't make bad mistakes. I also ride on the road with them to develop their traffic awareness. But helmets are a vital part of that.
I had several high speed crashes on my bike during school years. It was only luck that meant I didn't hit my head hard.
Please start making them wear helmets.