> Helmets increase survivability and decrease the degree of injuries in every respect.

Of course a helmet increases survivability of a head injury in a crash, that’s indisputable. But of course there is a window: some crashes are so minor that they are already survivable without a helmet; and some crashes are so bad that a helmet cannot help. And of course many injuries are not to the head at all.

The first-order effect of cycling helmets is definitely positive! But what are the second-order effects?

> To respond to the 'nuance' of your remark, that helmets change rider behavior for the worse, resulting in higher aggregate injuries - that is also incorrect.

There is evidence that they decrease the number of cyclists; and there is evidence that they change the behaviour of drivers.

When Western Australia imposed cycling helmet laws safety got worse: http://www.cycle-helmets.com/