I agree with you (surprise!) about making it mandatory. That's a family decision, not a governmental one. I disagree with your characterization about what the shot should be called.
Wow! I even agree with you for once. I've seen the idiotic commercials for this on TV and nowhere does it mention that this is about an STD. The ads have these 20-something year old women saying they want to tell their mothers about this, but if their mother is married to their father and has been in a monogamous marriage for 20 plus years there is no reason to get teh shot.