Can I suggest an alternative way to look this - who kills cyclists?
Answer 1. If cyclists kill themselves, they need to wear helmets*. Nothing else can help (except stop cycling).
Answer 2. If other road users kill cyclists, helmets aren't the answer. Other road users need to modify their behaviour.
The stats say it's answer 1.
Stats:
2019 stats for the above categories:
- 14 cyclists did the deed all on their own
- 85 had the help of another vehicle
- 1 poor bugger got hit by another cyclist. Doh.
= 100 cyclist deaths in total.
Serious casualties have even worse ratios towards other vehicles doing the damage:
- 265 cyclists seriously injured themselves
- 4,042 had the help of another vehicle
- 25 cyclists hit pedestrians
= 4,332 cyclists seriously injured in total.
Source:
Detailed statistics about reported personal injury road collisions for Great Britain, vehicles and casualties involved.
www.gov.uk
(follow the RAS40004 link)
* Inexperienced children and oldies pushing the envelope might fall into category 1, but it's not the majority of cyclists. You could argue for some limited mandatory helmet wearing especially for children learning to ride.