The Dutch and Danish make interesting case studies because their cultures are largely dependent on bicycles for personal transportation. Bicycle helmets are extremely rare in either country. An astute mind might then question why we Americans feel that bicycle helmets are a safety imperative everywhere and always, yet two countries with far more experience with bicycle transport do not.
The answer has a lot to do with our differences in infrastructure. Dutch and Danish roads are designed and built for mixed transportation modes. American roads are car-centric, and the lack of built-in accommodation makes biking a much more dangerous affair here, and in my opinion makes helmets mandatory for American road biking.
However, you might note in my earlier comments that I took pains to state that my kids are riding in a neighborhood park. Hence my question to you, which I note you didn't take a stab at. I'll answer it for you: yes, my local pedestrian park is safer than Dutch city streets. I've spent a good amount of time in the Netherlands, enough to be comfortable letting my kids biking there without helmets there (the same as Dutch kids do), and certainly enough to be comfortable allowing them to do so here in our arguably safer neighborhood park.
Another reason not to panic can be had with a bit of research into the comparative risks of head injury in everyday activities. For example, [1] is a frequently cited study from Australia (where road infrastructure is very similar to the U.S.) that found un-helmetted biking to be slightly safer than riding inside a car, and further finds evidence that mandatory helmet laws increase the health burden of a population by discouraging a healthy amount of outdoor activity. This is just one example.
But you know what's really dangerous? Trampolines. Our eleven-foot trampoline is by far the most dangerous thing in my possession. My kids are far more likely to be injured on the trampoline than anywhere else. My orthopedic surgeon (yes I'm a semi-regular patient due to a snowboarding accident) has trouble even discussing it with me, barely able to hide her disgust at my justifications.
So why do it? What's the reward for letting my kids risk life and limb on their trampoline, or for not weighting them down with security gear before they can go bike in the park? I hope I don't need to spell this out for you. Maybe it can suffice to point out that both my girls are now competitive gymnasts. I have an eight-year old who can do pullups and jog half a mile. My older child can do things on the uneven bars that I consider superhuman. These are kids who are glued to computer screens for much of the day, which is a far greater health risk, but by raising them to enjoy physical activity freely and spontaneously, I have a valuable tool in my fight to keep them healthy. That's the reward.
By the same token, the relatively small price of wearing lightweight ear plugs and non-prescription glasses buys me more acute hearing, which I prize highly, and has saved me from at least one eye injury. Plus, the glasses make me look smarter :)
Now, compare these risk/reward considerations with something like, say, tobacco smoking, perhaps the most egregious example of out-of whack risk/reward insanity there is. Odd as it seems, I've had my helmet policy questioned by smokers, on one occasion by someone with a cigarette in hand. The mind fucking boggles.
Again, if you're actually interested, I encourage you to do a bit more digging yourself. Humans are notoriously bad at evaluating risk and reward at the margins, and most of us entertain at least some nonsensical beliefs and behaviors as a result. A little knowledge can go a long way in this regard.
1 - http://www.sciencedirect.com/science/article/pii/00014575960...