"It is basic fact however, that if you fall on your head wearing a helmet it will help protect it."
It's not a basic fact at all, since we don't know if it increases the chance of
(a) falling/being hit (studies show that people take more risks when wearing a helmet, and that drivers drive closer to cyclists wearing helmets)
(b) hitting your head in the event that you do fall (we have primeval instincts to protect our skulls - do helmets impact on these; it makes your head a larger target)
"It is a hard shell which will reduce the impact on your skull. That is beyond debate."
Actually it's not a hard shell, it's a compressible layer of polystyrene. The few mm of polystyrene compress in order to absorb a limited amount of energy. A hard shell is NOT an effective design.
" Aside from the £10 cost, I fail to see a downside."
So I take it you wear one when you are driving? Because apart from the £10 cost I fail to see a downside.
"Helmet wearing is completely separate from road safety training, which of course is vital. One does not preclude the other."
They are not separate. Insurers of cycle events typically require cyclists to wear helmets. There is no check that a cyclist is competent. Clearly there is a desire to reduce risk to cyclists, for various reasons, liability, compassion, etc. The existence of a £10 safety product means that in fact in most cases the advice to 'make sure your child wears a helmet' is the only cycle safety message that gets through, particularly in relation to children.
One typically does preclude the other. The parents of this boy, www.nottinghampost.com/heart-ripped-says-dad-son-s-inquest/story-20103421-detail/story.html who cycled from the pavement into the path of a car travelling at 60mph, while wearing headphones, setup a campaign to make it illegal to cycle without a helmet. www.putthingsright.org.uk This campaign also relates to another local boy who died when he joined a main road from a side road without stopping and was hit by a car.
Only one thing would have saved those boys' lives for sure, and it is NOT wearing a helmet, it is basic cycle training (and maybe proper cycle maintenance, e.g., brakes).
The fact is that children are statistically usually to blame in road accidents (this is the reverse of adults, where the motorist is usually to blame). The solution to this is proper training.
I have seen literally dozens of threads on here about cycle helmets. I have never seen a thread about cycle training. This is proof enough that helmets preclude cycle training.
Cycle helmets are a consumption-based 'solution' to a lack of ability (at least in respect of children). 90% of cyclist deaths occur in collisions with other vehicles. Only 10% (or around a dozen a year) involve things like falling off because of a pothole, cycling into a tree riding down a mountain, etc. Therefore the risk that your child, not wearing a helmet, falls off riding in the park, and dies, is vanishingly small. Cars are a vastly bigger threat.