That isn't the problem. The problem is it takes too long to run this hypothetical study from "Vaccinate 12 year old boys" to "These 50 year olds didn't die of cancer at the expected rates". Nobody wants to wait 40 years to run a study that says this thing we suspect is a good idea is, in fact, a good idea. 40 years is a long time. If you follow a patient for six months, they're easy to find. Maybe a handful of them move city once, but they remember they were in a medical trial, "Oh yeah, sorry, I will come in for the follow-up appointment". If you try 40 years it's hopeless. They move ten times, they leave the country, they've forgotten all about your medical trial. So you start with 100 patients and 40 years later you can only trace eight of them, and now your trial is statistically invalid.
The existing efficacy demo for HPV vaccination against cervical cancer relies on the fact that Pap smears are a thing to get answers in just a few years not decades. The smear test gets us a bunch of cells that a pathologist can look at under a microscope and inspect to see if they're normal or maybe "pre-cancerous" meaning they aren't normal but they are not yet cancer. And we know (from having tried it) that if we just ignore it some of that not-yet-cancer turns into cancer and kills people. So if we see that in a smear today you'll get called back and they'll treat it, even though you haven't got cancer.
This means they could give girls an HPV vaccine and then not only show that those girls didn't get the strains of HPV vaccinated against as often as unvaccinated peers, but further show that they don't get as much not-yet-cancer. And _by implication_ that means it protects against cancer.
There is no smear test for these less common cancers in men. If there are pre-cancerous cells we don't see them. We only find out about the cancer, years and often decades later.
I think the "anywhere on the body... technically, this has not been proven." is also an infelicitous bit of wording. The links to anogenital cancers have been studied pretty thoroughly. There's less data on the head/neck/throat ones and virtually none at all on the vaccines' possible effect on warts elsewhere on the body.
It's presumably all the same mechanism whereby HPV infection stresses cells and eventually causes cancer, but it's much further from "proven".
The existing efficacy demo for HPV vaccination against cervical cancer relies on the fact that Pap smears are a thing to get answers in just a few years not decades. The smear test gets us a bunch of cells that a pathologist can look at under a microscope and inspect to see if they're normal or maybe "pre-cancerous" meaning they aren't normal but they are not yet cancer. And we know (from having tried it) that if we just ignore it some of that not-yet-cancer turns into cancer and kills people. So if we see that in a smear today you'll get called back and they'll treat it, even though you haven't got cancer.
This means they could give girls an HPV vaccine and then not only show that those girls didn't get the strains of HPV vaccinated against as often as unvaccinated peers, but further show that they don't get as much not-yet-cancer. And _by implication_ that means it protects against cancer.
There is no smear test for these less common cancers in men. If there are pre-cancerous cells we don't see them. We only find out about the cancer, years and often decades later.