The other half of it is, Even though the batters started hitting instead of striking out, they're mostly hitting singles or doubles instead of home runs. So it's easier to prevent runs from being scored (in this analogy, runs are deaths)

Relatively recently, gardasil (the vaccine most people think of) was approved for people up to the age of 45.

Of course it's only really important pre exposure, but you should still go and get it

There are hpv vaccines in various stages of trials, all the way to 24 valent vaccines