We do have proof of humanity once before successfully eradicating a virus, namely smallpox: https://en.wikipedia.org/wiki/Smallpox#Eradication
>In 2017, Canadian scientists recreated an extinct horse pox virus to demonstrate that the smallpox virus can be recreated in a small lab at a cost of about $100,000, by a team of scientists without specialist knowledge. This makes the retention controversy moot since the virus can be easily recreated even if all samples are destroyed. //
HPV is probably the best example that exists of an infection being linked practically 1:1 to a cancer. See more information here[1].
If you have knowledge of any other significant sources of cervical cancer, please share them.
And yes, no cancer can be eradicated, ever. Life finds a way.
https://www.cdc.gov/hpv/parents/cancer.html
>HPV cancers include cancer of the cervix, vulva, vagina, penis, or anus. HPV infection can also cause cancer in the back of the throat, including the base of the tongue and tonsils (called oropharyngeal cancer).
However, practically all cervical cancer is caused by HPV. Without HPV cervical cancer would be extremely rare, because it's going to need several quite uncommon random events to coincide, the virus is "deliberately" meddling with the copying mechanics inside cells, that's how a virus propagates, without a virus those changes have to happen entirely by accident, maybe a series of cosmic rays.
So it's not _that_ hyperbolic to say this eradicates the cancer itself.