I think not many people will argue with you that helmets reduce head injuries (unless they aren't put on properly). However, I think you're missing the bigger picture that mandating helmet use (or even strongly encouraging use) can lead to less people cycling. There are studies in the pdf on exactly this happening in Aus and NZ
How about Cycling UK for references? https://www.cyclinguk.org/sites/default/files/document/2017/11/helmets-evidence_brf.pdf
I think not many people will argue with you that helmets reduce head injuries (unless they aren't put on properly). However, I think you're missing the bigger picture that mandating helmet use (or even strongly encouraging use) can lead to less people cycling. There are studies in the pdf on exactly this happening in Aus and NZ