5-year survival rate of throat cancer is 82%, 5-year survival rate of cervical cancer is 92%, and incidence of HPV-related throat cancers among men is higher than cervical cancer on it's own and rising (probably due to changes in sexual behavior) [0]. While total incidence of HPV related cancers is higher in women than in men and that's bad enough, there is not a lot of difference. It's a problem on its own.
It’s the incidence that is important here. So while there’s higher survivability for cervical cancer, there are many more deaths. (At least until this vaccine)
So people are concerned with the risk of having throat cancer more than the risk of death if they get it. And this seems reasonable. As I have a very high risk of death in many improbable situations and I care more about lower risk of death in very common situations.
10k cases of throat cancer in men each year in the US [0]. Although HPV-related cancer, oropharynx, is less than that and harder for me to find a good incident rate. Almost 14k cases of cervical cancer in women each year in the US [1]
But that's my point: the incidence of cervical cancer in women and throat cancer in men is in the same order of magnitude, but the incidence of cervical cancer is stable or even declining due to screenings and HPV vaccination, while the incidence of back of the throat cancer in men is five fold higher than throat cancer in women already. And what's more, it is rising - also five fold over the past decade - due to (unprotected) oral sex becoming more common.
The vaccine prevents against up to 9 HPV, including many genital wart [0] strains.
So I was wrong about herpes but my point was that it protects males against STIs and is just a handy vaccine to protect sexually active men against something they don’t want (some genital warts) and that seems like a greater motivator than reducing transmission to protect women from cervical cancer.