The case in favour of bike helmets is nowhere as clear-cut as most people think. (My husband is a keen non-helmet wearing cyclist and has facts and figures on this coming out of his ears).
BUT he tells me that the type of fall for which helmets are designed are just as likely from a scooter as from a bike. So, tortoise, you are probably more rational than the rest of us who don't make our kids wear helmets on scooters.
But please, please, please - all helmet-using parents - make sure your children know that they must remove them when they are not on their bikes/scooters. They are NOT designed for general, rough and tumble play. A child in Denmark died from strangulation due to his helmet getting wedged in a climbing frame. The shape of the helmet makes your head bigger than you think (so liable to get stuck) and the straps are a strangulation hazard.
Now I will get off my particular high horse with respect to helmets and let tortoise have her thread back.