Remember kids... always wear a helmet. (The almighty bikeradar helmet thread)

Your first link:

It is estimated that up to 85 percent of head injuries can be
prevented through proper usage of helmets

http://www.cyclehelmets.org/1131.html

In June 2013, US federal agencies The National Highway Traffic Safety
Administration (NHTSA) and the Centers for Disease Control (CDC)
decided that they could no longer justify citing the claim that
bicycle helmets reduce the risk of head injury by 85%. The agencies
had been challenged under the Data Quality Act to show why they
ignored later research, none of which had produced such convincing
results. Other US Government agencies are expected to follow suit.
(GGW, 2013)

Head injuries are not the rare event you want to think they are

Fermi estimate time. Let's say for the sake of argument that your aans.org link is a proxy for UK stats, and the hospital admissions is a proxy for KSI. About 1 in 6 hospital admissions among cyclists in your study is for a head injury. UK cycling KSI rate is about 1 per 500,000 journeys. That makes head injuries worthy of hospital treatment about 1 per 3M journeys, or 3×10^-7 per journey.

I leave it to the reader to decide whether that makes cycling related head injuries rare or commonplace. If you bought two tickets for the National Lottery, your probability of winning either the jackpot or the second prize is also about 3×10^-7

You continue to fail to respond to the points I've made, continuing to satisfy yourself with this endless cry of helmets put people off cycling.

So I'll argue against that- just this once- as evidenced by the follow-on resurgence of cycling in Australia, Canada and other places with compulsory helmet laws.
http://www.publish.csiro.au/he/HE11178
(amongst others).

Hey, that is a bit unfair. You have put out a dozen or so links to academic articles most of which are only available to read by paying a significant fee. To make sense of these articles we need to read them and read follow up commentaries published in the journals and elsewhere. That takes time and I will do what I can with each of them in time.
The CSIRO study linked to above supports the case that helmet laws restrict levels of cycling and growth in cycling.

You may not be aware of the level of academic political warfare being waged on this issue, indicated in some of the links you have posted. Not least over the editorship of Injury Prevention journal or between UNSW and University of Sydney. People who have experienced such academic politics say it is more like that of Saudi Arabia than the mild goings on in Brexit Mania or Trumpism.

And if we're all honest- Helmet or no is not going to change inactivity levels in a wider spectrum of the population.

But that is precisely what happened in Australia when helmet laws came into force 25+ years ago. Child cycling participation dropped by about 40% or more in a couple of years. Most of the "resurgence" since then has been in adult sport cycling not children and everyday cycling except where there has been high levels of government intervention and promotion.