The vaccine actually works. If it lowers your risk of fairly nasty cancers (and other less debilitating—-but embarrassing—-conditions), while earning them a few bucks, isn’t that a solid win-win scenario?
At least it’s not the usual trope about how Big Pharma is hiding all the cures....
There's no 40 year record, obviously, since the vaccine itself is only about 25 years old. However, the extant data shows a giant drop (30-50%, depending on age group), in HPV infections. That's already a huge win for everyone but genital warts, and we haven't even gotten to cancer.
The link between HPV infection and cancer is also well established. There's good quality observational data: one clever study looked at cancer incidence in the spouses of HPV patients (Mirghani et al., 2017). The molecular mechanisms are at least partially understood and seem to overlap with what we know about other kinds of cancer too.
Maybe it "works" but the actual benefit is minuscule? Nope. Even estimates based on the older, less effective versions of the vaccine find that it's cost-effective. See, for example, Sanders and Taira (2003): https://www.ncbi.nlm.nih.gov/pubmed/12533280
In short, all of the available evidence suggests it's a highly effective intervention, with minimal risk to individuals and big gains for their own health and the population's. You don't have to take my word for it either. You can look at the CADTH reports (Canada; CADTH.ca), NICE (UK; https://www.evidence.nhs.uk/search?q=HPV) and basically every other set of guidance on the topic, which all recommend vaccination.
EDIT: Ok, sorry about the snark, but I do think this is actually a constructive comment.