I suspect that we would be better off if there was a social norm of everyone wearing helmets all the time.
No, you mean that there will be some decrease in injuries/deaths. Whether we would be "better off" requires considering the cost part of the equation as well (not to mention picking the metric for "better").
For example, a similar social norm of never ever going swimming would also result in a decrease in deaths. Would it make us "better off"?
I would agree with the social norm of never ever going swimming. In fact, I have a very hard time understanding why people are so willing to basically immerse themselves in an environment so deadly to human beings. I certainly never do it myself.
A 2006 study showed that “280,000 people in the U.S. receive a motor vehicle induced traumatic brain injury every year” so you would think that wearing a helmet while driving would be commonplace. Race car drivers wear helmets. But since almost no one wears a helmet while driving a regular car, you probably fear that if you wore one you would look silly, attract the notice of the police for driving while weird, or the attention of another driver who took your safety attire as a challenge. (Car drivers are more likely to hit bicyclists who wear helmets.)
The $30+shipping Crasche hat is designed for people who should wear a helmet but don’t. It looks like a ski cap, but contains concealed lightweight protective material. People who have signed up for cryonics, such as myself, would get an especially high expected benefit from using a driving helmet because we very much want our brains to “survive” even a “fatal” crash. I have been using a Crasche hat for about a week.