There isn't much question that helmets reduce injury. The larger question of "should they be mandatory" is still open (with a strong lean towards "no.")
From the first article.
"Even most opponents of mandatory helmet laws advocate helmet use, but they say that the negative consequences of helmet laws outweigh the benefits."
From the third.
"If you consider the entire body of research rather than just one study, and look at both head and neck injuries, helmets only reduce the risk of injury by about 15% to 45% ."
Wearing a helmet would also improve the safety of people driving or walking around. But strangely we don't hear all the nagging lectures for people to wear a helmet when they are driving or walking to a corner store, whether or not it's on a quiet street in fine weather.
Negligible for walking. Its different to be hurtling along at 20mph on a contraption of pipes, gears and chains and hit a storm drain, launching headfirst into the back of a parked car, than to trip and skin your knee. One requires a helmet to survive.
And driving - there's airbags and the steel cage and belts and padding. Another storey altogether.
Walking is pretty dangerous: you could be walking and spontaneously stumble, or slip on wet leaves, and clip your temple on a fire hydrant. That's it for you! Walking is quite dangerous, and is in fact has the highest rate of injuries and fatalities per mile traveled. That's mostly because pedestrians get hit by cars, but that's surely an even better reason to get pedestrians to wear helmets. What if you get hit by a car while walking?
Yes, that seems odd. Maybe because of the speed difference - per-mile stats weight pedestrian trips more, because they take longer/are exposed to environmental hazards longer (e.g. getting hit by a car).
Not sure which statistics you refer to, but one explanation is simply that many pedestrian accidents (falls) are very old people. They fall, they break pelvis, they are immobilized, they die.
There's a lot of nagging about seat belt usage in cars. For just about as good reason as for wearing a helmet when biking. Even when driving to the corner store.
http://www.washingtonpost.com/national/health-science/do-bik...
http://www.californiahealthline.org/insight/2015/bicycle-hel...
http://greatergreaterwashington.org/post/19036/feds-will-sto...