I imagine that it may be related with the interaction between viral E6/E7 and epithelium's RB and P53 with respect of the later expression levels in cells with "high activity", opposed to the expression levels of these proteins in other epithelial differential state. I would start from there.

Papillomaviruses are absolutely species specific and tissue specific. HPV will infect and replicate in a fully differentiating squamous epithelium only. The virus infectious cycle is rather complex and can explain the duration of an HPV infection. It involves both temporal and spatial separation of viral protein expression. The virus first infects a keratinocyte in the basal layer of the epithelium as a consequence of microtrauma, i.e., an abrasion of the epithelium that exposes the basement membrane and basal cells. In the proliferative compartments of the epithelium, there is a phase of plasmid maintenance, the virus and cell replicate together, and the viral copy number is maintained at around 50 to 100 copies in the daughter cells. For the oncogenic viruses, in particular, viral gene expression is very tightly controlled during this phase. As long as the cell is dividing, the high-risk HPVs control the expression of their viral proteins very tightly. The E6 and E7 oncogenes are thus expressed at very low levels. When the host cell stops dividing and begins to differentiate into a mature keratinocyte, this provides a signal to the virus to activate all of its genes to increase the viral genome copy number to the thousands. In the case of incipient malignancy, control of E6 and E7 expression is lost, and gene expression in the cell becomes deregulated. In the top layers of the epithelium, all of the viral genes, including those encoding the L1 and L2 proteins, are expressed, and many thousands of viral genomes are encapsidated; these exit the cell as infectious virus particles. The time taken from infection to the generation of infectious virus is at least 3 weeks. HPV thus has a very long infectious cycle, has no blood-borne phase, and does not cause cell death.