It's not just high speed that makes helmets useful: you can get a brain injury just falling over when you're stopped, if you hit your head on something hard (like asphalt or concrete, which most roads and sidewalks and curbs tend to be made of).
People's bodies simply were not evolved for a concrete environment. Helmets are how we deal with that.
You'd be surprised at how good people are instinctively at not bonking their head on stuff. In an ordinary bike accident -- e.g. swerving for something unexpected, and then falling -- you'll not hit your head on anything. Road rash is no fun either but you're not more likely to hit your head on a bicycle than you are when just walking around.
>In an ordinary bike accident -- e.g. swerving for something unexpected, and then falling -- you'll not hit your head on anything.
You can't say that with 100% certainty. There could be a curb there, and you might not catch yourself properly, and hit your head on it.
Sorry, but I'm not going to bet my life on your feelings of "how good people are". Putting on a helmet isn't some kind of huge burden; it's no different than wearing a seat belt in a car.
>Road rash is no fun either but you're not more likely to hit your head on a bicycle than you are when just walking around.
When you're walking around, your head isn't traveling 10-30 mph. The relative likelihood is irrelevant, what's important is velocity.
People's bodies simply were not evolved for a concrete environment. Helmets are how we deal with that.