it is my vague recollection from articles i've read that hpv is typically cleared by the body after some period of time.
a quick google of "hpv clearance rates" appears to yield several articles that relate to this, including, for example..
i've only given this the most cursory skimming, but it seems to imply that the body does clear hpv.
this does not sound remarkable to me. we know of many viruses that yield chronic infections (hiv, hep, herpes, etc, etc.) and many that regularly infect us, and we regularly clear, with or without medical treatment (flu, cold, etc).
so i'm still hoping someone qualified can speak to whether the hpv vaccine has a possible benefit if given to older adults. i don't feel qualified to read the sources myself, and hope someone who is can offer an interpretation.
some of the discussion seems to conflate the issue of whether the vaccine would have some efficacy with the separate question of whether that efficacy is worth the $300 or $400 it might cost per person to administer.