HPV 16 & 18, together account for about 70% of invasive cervical cancers. While 10,000 cervical cancers a year in the US may seem small compared to other causes of death, 10,000 people are a lot of people. Especially, now there is a vaccine that could prevent 7,000 or those cancers. There are about 4,000 deaths a year from cervical cancer at this time. At one time cervical cancer was the most common type of cancer among women and the leading cause of cancer death. This has dramatically changed with modern medical screening and treatment for non-invasive cervical cancer, or pre-malignant dysplasia. As a matter of fact, a significant amount of health care dollars goes to screening and treating conditions before the cancer develops. So yes, there are only 4K deaths and 10K cancers a year, there are thousands that never get invasive cancer due these efforts.
Bear in mind also there are complications to female fertility and ability to carry a pregnancy with some treatments. The biopsies to determine if a woman has cervical cancer are not pain free (physically or for the wallet book). The mental stress of having to follow-up with their doctors of these exams and biopsies every 3 months is costly in emotional and financial capital. And this is only to deal with the cervical cancer aspect.
HPV 6 & 11 also causes genital warts (together about 90% of the cases). Genital warts are embarrassing. They can grow to really impressive sizes. Removing them will not get rid of the potential for more to grow. On the other hand (so to speak) most genital warts are small and not noticed, easy to transmit if you don’t know you go it. Treatment requires multiple treatments and trips to the doctor. HPV 6 & 11 can also cause changes in cells on the cervix that might be considered precancerous and all the screening and treatments above may be needed.
The Gardasil vaccine is a vaccine against HPV 16, 18, 6, and 11. The vaccine was highly effective (>95% for cervical cancer, vulvar pre cancers, and genital warts) in clinical trials and if used on a national basis could indeed reduce over half of the invasive cervical cancers it would also reduced the health care cost that go into treating all the premalignant conditions (that never progress to cancer because of aggressive medical intervention). This will be the greatest impact of the vaccine. Keep in mind that the vaccine will also prevent about 90% of anogenital warts. The prevalence of genital warts is about 1% of the US population or some where around 3 million people.