TonyR wrote: Now in BMX nobody has done the studies AFAIK but why do you think that common sense works there and not on the roads? Certainly the helmets make your head a bigger target in an offie and you can almost guarantee that riders would not try such big stunts without the assumed protection of helmets.
I was going to post about BMX as a modern sport, but pjclinch beat me to it. What I will say is that the sort of BMX riding that kids do, and have done since the invention of BMX is often without helmets.
It's anecdotal, but there was an informal BMX track near the village in Essex where I lived, and lots of kids 'played' there on their bikes, and I seldom saw any helmets on the kids that used it. BMX club riders in the area wore helmets, but they didn't always when they were just riding around the village.
When BMX first became a thing in the USA, people didn't wear helmets. My friends and I built a BMX track in an abandoned quarry in the late 70s, and spent hours and hours there, jumping bikes, improving the track, racing on it, etc. I started with cheap and cheerful toy shop bikes, and broke a few frames, but never seriously injured myself. The only injuries I recall were a couple of kids who broke arms or collarbones doing it. I didn't know anyone who wore a helmet. The only protective gear that I can recall anyone wore was gloves.
I think that it is reasonable to wear protective equipment when doing activities that present higher risk. It is likely that the use of protective equipment influences behaviour, but we do not know to what extent. To say that BMX riders are injured more because they wear protective equipment has at least a couple of logical fallacies.