I didn't (initially) wish to comment on forcing anyone to use a vaccine, only to your contention that HPV is neither contagious or deadly, when it's manifestly both. As to whether sexually transmitted infections don't represent imminent threats, HPV is about as contagious and dangerous as other viral diseases with latent courses, such as hepatitis B (transmitted through sex, vertical transmission from mother to newborn, and shared needles - but not by coughing at Disneyland), vaccination for which has long been required in every state I've worked in.
Other sexually transmitted viruses (like HIV) can reasonably be construed to present imminent threats in areas and among populations where they are endemic.
I suppose it's reasonable to argue we should make a list of which vaccines are required for school entry and which aren't. You mentioned flu vaccine above, for example, which has varying efficacy depending on antigenic drift of the virus from year to year, though even in bad years the vaccine seems to be effective at preventing invasive (deadly) disease in high risk populations, which include young children. Should we cross vaccines off the list if they are periodically less effective (but still effective) some years even though the disease is still deadly and manifestly contagious? Should we eliminate hep A because even though it's contagious it's just about never deadly? Or do we keep things simple and state we should vaccinate kids against diseases that are either manifestly contagious and onerous, deadly, or both?
I've periodically have patients dying of HPV-related cancers - not a lot, but it's out there. I suspect they would have appreciated universal vaccination had it been available for them before their first sexual contact and while they were getting routine childhood doctor visits, after which the utility of the vaccine goes down substantially.