Please re-read your first link. "Most HPV infections of the cervix are cleared rapidly by the immune system and do not progress to cervical cancer (see below th

Please re-read your first link. "Most HPV infections of the cervix are cleared rapidly by the immune system and do not progress to cervical cancer (see below the Clearance subsection in Virology). Because the process of transforming normal cervical cells into cancerous ones is slow, cancer occurs in people having been infected with HPV for a long time, usually over a decade or more (persistent infection)." 1) Not every person with HPV gets cervical cancer. 2) Many people will get into a monogamous relationship, it will not spread further. 3) It is not necessarily spread in every sexual encounter. Therefore eradication is definitely possible.