In a car you have airbags, which are sort of like an external helmet.
As for walking, there are a lot more things that can go wrong on a bike. You can hit a pothole, get your wheel caught in a train track, slip on an oil patch, get doored, have your chain get stuck, not be able to clip out of your pedal, get something caught in your spokes, take a corner on some sand, hit the ground with your pedal, etc.
These things aren't very likely, but any of them provides a fair chance to lose control of your bike and then hit something or the ground at a decent speed. The more traffic you ride in the more likely something will happen. And if you ride every day to commute, you'll almost certainly have some kind of incident sooner or later.
Personal anecdote section:
I bike commuted for 2.5 years in the south bay without any major incidents. Later, I had been bike commuting in SF for about a month when I had an accident that involved hitting my head on a parked truck and then the ground (at least I think). The helmet ended up slightly scraped up. I don't know how badly my head would have been injured without it; it may have been just a scrape as well. But I'm quite happy I didn't get to find out.
As for walking, there are a lot more things that can go wrong on a bike. You can hit a pothole, get your wheel caught in a train track, slip on an oil patch, get doored, have your chain get stuck, not be able to clip out of your pedal, get something caught in your spokes, take a corner on some sand, hit the ground with your pedal, etc.
These things aren't very likely, but any of them provides a fair chance to lose control of your bike and then hit something or the ground at a decent speed. The more traffic you ride in the more likely something will happen. And if you ride every day to commute, you'll almost certainly have some kind of incident sooner or later.
Personal anecdote section:
I bike commuted for 2.5 years in the south bay without any major incidents. Later, I had been bike commuting in SF for about a month when I had an accident that involved hitting my head on a parked truck and then the ground (at least I think). The helmet ended up slightly scraped up. I don't know how badly my head would have been injured without it; it may have been just a scrape as well. But I'm quite happy I didn't get to find out.