There are on only two paragraphs about this in the Wikipedia link you gave, and the second one ends:

Elvik writes "When the risk of injury to head, face or neck is viewed as a whole, bicycle helmets do provide a small protective effect. This effect is evident only in older studies. New studies, summarised by a random-effects model of analysis, indicate no net protective effect".

I'm guessing you didn't read it and assumed it supported your preconceptions?

(Going to politely revoke my snarky response to your snark)

I specifically mentioned head injuries (TBIs) - there are two meta analyses listed, the point you listed went beyond that (to include neck and face injuries). The other meta analysis also supported its TBI-reducing benefits.

Edit: If you're looking for the pertinent line from the analysis:

"With respect to head injury, the answer is clearly yes, and the re-analysis of the meta-analysis reported by Attewell et al. (2001) in this paper has not changed this answer."

Apologies for any snark.

What you actually said was, "Helmets are pretty universally known to reduce traumatic brain injuries."

This is wrong and not what you are now saying. You are now saying that among people who have suffered brain injuries, helmets are known to reduce traumatic brain injuries.

If the helmets make it more likely that you suffer an injury in the first place, it's not really a consolation that they mitigate the effects. There are actually reasons why many people oppose compulsory helmet laws.

I'm sorry, but I'm having a hard time parsing what you're saying. Both meta analyses supported my initial point.