"This is because cycling is a healthy, low-risk activity akin to walking or swimming"
I agree with others that it depends on where you are riding the bike. If you are on roads, going down hill etc, then correct helmets, not bought from discount shops, fitted properly, will prevent a serious head injury.
Most people who have serious aquired brain injuries are kept in "institution" type places, so we don't see the outcome of simple, preventable, aquired brain injury. If we did, we would be removing risk when possible. There are numerous conditions caused by less serious head injuries, which again, we don't tend to talk about much.
I have researched bike safety, in terms of scooters and under 50cc mini moter bikes, as my DD, with SN wants one for her 16th Birthday.
Many people do not realise that when riding a pedal bike at speed you can be going faster than a scooter. If you are on the road and hit by a car, there is no difference between a mini motor bike and a pedel one, except on a motorbike, you will be safely dressed and trained to ride it safely.
I think that it is better to start road safety young, as trying to tell a teenage boy (these have the highest serious injury and death rate, during any activity), how to do anything safely, is near impossible. It needs to be drummed into them as soon as they begin any activity.