When I looked into this a few years ago I turned up Prevention of Head Injuries to Car Occupants: An Investigation of Interior Padding Options (McLean et. al. 1997). The improvement in interior padding and airbags since 1997 is probably enough to bring the benefit of a bicycle-style helmet down to just a few percent injury reduction.
But even assuming its as high as 10%, Nick Beckstead wrote:
You allegedly get 1 micromort from driving 230 miles. Say that takes 4 hours, and say you get to reduce 10% of that by wearing the helmet. Then wearing a helmet for 1 hr saves your life with probability 1 in 40 million. So the question is whether you prefer a 1 in 40 million chance of saving your life or the convenience of not wearing a helmet in the car for an hour.
If you valued your life at $40M, then the question would reduce to whether you would be willing to wear a helmet for an hour if it saved you a dollar (neglecting safety benefits). I wouldn't wear a helmet for an hour for a dollar, and would pay a dollar to avoid wearing the helmet. Since all these estimates are average or conservative, that suggests it is not worth it to wear a helmet (at least for me).
Galaxy brain take: one man's modus ponens is another man's modus tollens - he wouldn't wear a car helmet, so by the same logic, it's not worthwhile to wear a helmet while biking: https://www.forbes.com/sites/carltonreid/2018/10/21/i-do-not-wear-a-bicycle-helmet/
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.