Thompson, Rivara and Thompson reviewing largely their own (flawed) work? Really? Still in 2025, that's all you got? I don't like to dismiss things based on the researchers, but I'll make an exception for the parents of the "90% reduction in head injury" BS: they really are not neutral or objective AFAICT, and their work has been rebutted almost as many times as Jake Olivier's, so I'm not going to take the time to do it again myself, and just point you at one of many:
https://www.cyclehelmets.org/1243.html
Here's another couple of papers in the bmj
https://www.bmj.com/content/321/7268/1055
That's only the Hospital Episode Statistics, not even all reported road casualties, so it ignores the question of whether helmet use makes cyclists more likely to end up in hospital, plus there's not enough data published to verify its conclusions, plus it cites Thompson, Rivara and Thompson uncritically, so its conclusions should be regarded with suspicion IMO.
As well as only being hospital data, only half the collisions in the dataset have helmet use recorded, plus it finds a reduction in facial injuries which makes me doubt it. How many full-face helmets do you see cyclists using? I can't remember the last time I saw one not on an MTB track.
Hospital data again, not population data, again, plus cites Thompson Rivara Thompson and Olivier, so I doubt how neutral a position they started from.
I have been unable to find any medical research that does *not* come to the conclusion that cycle helmets reduce injury.
None of the research you link comes to the conclusion that cycle helmets reduce injury at a population level. They're mostly studying the wrong question, an easy win, but beside the point. The stuff you link shows that if you have a bad enough crash to end up at a hospital, or in some cases only that you end up at one with a head injury, then use of a cycle helmet will probably mean a reduced injury severity. That's not the debate. It's whether increased helmet use means a reduced chance of injury, overall, on average, at a population level.
Think of it like this: would you want to use a helmet if it halves the severity of a head injury but makes you ten times more likely to suffer one? The research you're looking at is only considering the first half of that question.