There are roughly a dozen high risk HPV strains responsible for cervical cancer. These strains promote hyperplasia of infected cells by encoding E6 and E7, which potently antagonize tumor suppressor genes RB1 and TP53. Overtime the episomal viral DNA gets incorporated into the host chromosomes by the cellular DNA repair mechanism, which enables stable propagation of viral oncoproteins to daughter cells (according to this paper, about 80% of cervical cancer cases harbor at least one copy of HPV DNA in the chromosomes).
However, there are many more strains causing hyperplasia of infected skins, such as the strains causing common warts, flat warts, and genital warts, but none of them have been found to be associated with cancer. Is it because these viruses encode milder oncoproteins that don’t potently antagonize RB1 or TP53; because these viruses infect wrong types of cells which are refractory to transformation by E6 and E7 compared to cervical epithelium (oncogenes are context dependent. For example, EWS-FLI1 potently transforms mesenchymal stem cells into Ewing sarcoma, but causes senescence and apoptosis in more differentiated cells); or because the viral DNA do not incorporate into the host chromosomes (which sounds unlikely because incorporation of foreign DNA by DNA repair mechanisms is inevitable after prolonged exposure)?