'But if you vaccinate most teenage girls, then it WILL be mostly eradicated, isn't that the point?'
No, because the big transmitter was always the male, who is next to never aware he is carrying strains which can cause cancer.
And if you have 10% of the population of males who are never having sex with females, but only with males, who are still carrying the virus, you won't eradicate it and will instead see more and more of those males with throat cancer, which sadly isn't as easy to catch before it becomes cancerous, unlike cervical cancer.
Furthermore, these males having sex with men also increase their risk of anal cancer from HPV.