I have mixed feelings about this issue so I haven't posted yet. I've read everyone's posts and there is something to be said for every one of them.
Being aware that we have an international community on this forum, let me say that my comments refer to the USA. It's been almost 50 years since I lived in France, and I was only in high school then, so I have no useful information or opinions on other countries.
Should it be illegal to ride without a helmet? My instinct is to say no.
I don't especially like the fact that there isn't a switch to turn off the air bag in my car. I just might have a good reason for wanting one. Back when airbags were being developed, Joan Claybrook at the NHTSA got the manufacturers to put in powerful airbags because she wanted them to work even if seat belts weren't being worn. The auto companies wanted to see airbag and seat belt as a system, which would have meant less impact from the airbag. Who doesn't know someone who was injured by an unnecessarily violent airbag deployment?
So as far as freedom and rights go, I lean towards "that government is best which governs least." (Thomas Jefferson)
Yet there are laws that we have, and most of us accept, that govern individual behavior like this. Laws that say you have to cross a street at a crosswalk, for instance. They don't protect automobiles!
More to the point, please consider laws requiring children to wear bike helmets. A strong case could be made that this should be the parent's decision. Most states require children of some age to wear a helmet, but no one has voiced any serious disagreement about that.
So that's the legal stuff.
On the other side, there's personal choice. I wear a helmet on most every ride regardless of speed or distance. It has nothing to do with the calculation of odds. The odds are I won't have an accident involving my head, seeing as how I haven't had one in 65 years.
But here's what I've learned from playing poker, and from the absence of any such references, I gather there are not a lot of gambling folks on this forum. One simple dictum that every serious gambler must learn, and most amateur gamblers never do: you never gamble what you can't stand to lose. Even if I'm sitting there with a full house I don't gamble the rent money, because someone else might have four of a kind. And I don't take chances with my head, because it's the only one I've got.