General Discussion

"But the rise in net inconvenience would be much greater than the relative gain."

The inconvenience for an individual is the same. (probably slightly lower for the car driver, since he has a secure place to leave his helmet)

But the net inconvenience for society is larger because more people drive cars than cycles.

And the net social cost of not having car helmets is less because the lives saved are a much smaller percentage of the total inconvenience. Each life is as precious, of course, but each car life is divided by much more net inconvenience.

I threw in the thing at the end because I wanted to make the point that every aspect of traffic safety strikes a balance between convenience and deaths, so there's nothing odd in looking at the question that way. (To save the most lives we could ban going outdoors at all.)