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).