1) I get the impression that most people do most of their driving alone. And of the people in the car with you, it's mostly pretty close friends/family, whom you presumably are pretty comfortable around. As for random people seeing you through the window, I wouldn't think that that'd be too embarrassing, given that it's so fleeting and that you'll never see them again. So all in all, I don't see that there's too big a downside. Maybe it's just because it leads to the self-narrative of "I'm a weirdo"?
I happen to take great joy in being contrarian in rational ways haha. So if I drove I'd totally do this!
2) Different way of looking at it (for parents) - would you chose to put a helmet on your child?
(2) Below a certain age, yes (now at least) if I thought it added much safety value beyond a child's seat. Above this age, his choice but I would offered to pay for it.
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.