Including on bike helmet safety labels. Fact is, they really are designed for falls and not for collisions with motor vehicles. In that situation, they may just be a "better than nothing", possibly not enough to make any difference to the outcome.
So . . . you wear a helmet when driving? Because people get head injuries all the time in car wrecks.
You're right, though. Cars are fundamentally dangerous. High risk of violent injury or death, and, even in the best case, they subtly harm your health and longevity by encouraging a sedentary lifestyle. Damned expensive, too. Perhaps we should all just move to Rotterdam so we wouldn't have to deal with them so much.
yet statistically per-passenger-mile you're more likely to get a head injury while in a car than on a bike.
An argument can be made that you should wear a helmet of some sort in many circumstances where it's not required (or expected) today. Look at downhill skiing. It's still far from universal but no one (besides racers) wore a helmet until 20 years ago or so. I still don't wear one.
Depending on how fast you are going, a helmet may even help for hitting things. Quite a few people don't exceed 25 km/h on their bikes, especially in city situations. Similarly, if you are aware of a dangerous situation, then slowing down may give you some protection. It's absolutely not going to help if you are bombing along at 40 km/h and get doored, but at that point, nothing really will.
One thing that would help is taking the lane when going at those speeds. People don't normally drive their cars going 40 km/h in the door zone, so the same thing should apply when riding a bicycle.
My own sense is that the science seems pretty clear that, provided you are in a wreck, wearing a helmet greatly reduces your risk of serious injury and death. Helmets aren't perfect, and they may primarily be designed for lower-engery impacts, but even insufficient energy dissipation is better than zero energy dissipation.
There's a secondary claim that not wearing a helmet results in safer behavior than wearing one, and that outweighs any potential benefit. I'm not aware of any quality research to back that claim, and you'd never be able to get a study to pin the question down past an institutional review board, so I'm inclined to say that cuts very close to what we called a fundamentally unanswerable question back in my class on experiment design. (Well, actually we used the acronym most the time. ^_^ ) My personal sense is to think that expecting your garden variety distracted, chronically fatigued, or nonzero BAC driver to notice whether you're wearing a helmet in the first place, let alone modify their behavior accordingly, is giving them more credit than they've earned.