It's worth noting the benefits of HPV vaccination do seem to be quite real, though. In the US, >20% of the female population has a high-risk HPV infection [1], and cervical cancer runs at ~12k new cases and ~4k deaths a year [2]. A follow-up study found women vaccinated before age 17 had about 88% reduction in cervical cancer, with around 53% for women vaccinated at 17-30 years of age [3] (presumably later-vaccinated women had a high chance of already having an HPV infection so the vaccine wouldn't be useful).
I think potentially saving >3.5k lives and >10k cervical cancer cases annually in the US is a pretty good return if we can get widespread HPV vaccination, though of course we should also work hard to study and minimize vaccine side-effects. I'm similarly hopeful of news about EBV as a cause of multiple sclerosis [4], which is another situation where preventing a widespread infection might prevent rare but serious illnesses.
[1] https://www.cdc.gov/nchs/products/databriefs/db280.htm
[2] https://gis.cdc.gov/Cancer/USCS/#/Trends/1,2,73,1,3,value,23
[3] https://www.cancer.gov/news-events/cancer-currents-blog/2020...
[4] https://www.hsph.harvard.edu/news/press-releases/epstein-bar...