They definitely cut the prevalence of the subtypes they vaccinate for. the previously high-hitters for cancer (16, 18) are effectively reduced by a rate of something like 80% from vaccination. However other subtypes that the vaccine doesnt block could be behind the ongoing rise in cancer along with the unvaccinated.

That said -- I have yet to see statistics that show that the spread of HPV is down overall particularly for subtypes associated with cancer. That would be wonderful to see, but google/the CDC does not readily show such data to me, I'd have to keep digging

Now we do know that something like 91% of anal cancer (not colorectal) and 70% of throat cancer is HPV related according to the CDC. And unfortunately both throat cancer and anal cancer are in fact on the rise for all age groups and there is a hidden epidemic where young people are now getting it.

This to me would imply the possibility that the HPV vaccination is not effective currently -- either due to a lack of vaccination across previous generations or because of cancerous subtypes not covered by any vaccine.

https://seer.cancer.gov/statfacts/html/oralcav.html https://seer.cancer.gov/statfacts/html/anus.html

Prostate cancer is also seeking an uptick in young people https://seer.cancer.gov/statfacts/html/prost.html