My gut says that the performance in a vehicle collision will probably bring the head to a halt against a relatively immobile object, so the hat won't do much of anything as the crushable bits are crushed too fast to be effective.
I don't see how the latter clause follows from the former. You said that in the drop test, the impact reduction was roughly 25%. This isn't huge, but I can't say it "won't do much of anything." Were you thinking of something else to support your claim?
No other source, but keep in mind that helmets are tuned for a certain force level. Too durable and helmet does not reduce peak force as it does not crush. Too weak and it crushes quickly, again with little reduction in peak force. This should just empasize to use the 25% number here though since the forces are more representative.
Redacting "won't do much of anything" except as implied by 25%, but keep in mind that if peak accelerations are much higher than the given case, the helmet will be less effective due to the above. This may or may not be the case in car crashes depending on speed.
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.