Like RAM, I was thinking of polio too. To "eradicate" a virus, you have to vaccinate basically
everyone who would come into contact with it (while quarantining those infected) and pray to god that it doesn't mutate. They found a pretty cheap way to make smallpox and polio vaccines and had the willpower to do it (I could also mention the standard Measles-Mumps-Rubella vaccine that children get here in the US too, nobody gets those diseases here anymore either).
Viruses are tricky things and if they mutate a significant amount then no vaccination will keep you from getting infected. Added to that, some viruses can jump species, so even if you vaccinated every human on the planet, some non-human animals could still get the virus and it would continue to live and possibly mutate and jump back to humans in a form that the vaccine doesn't prevent against (or come back when people quit getting the vaccine - polio vaccines aren't standard in the US anymore...).That's where HIV is such a hard thing to kill - it mutates like crazy even while inside the host.
HIV wouldn't be the best idea for controlling people's sexual deviancy though - it's a reasonably hard disease to contract. Even if you have sex with someone who has HIV your chances are pretty low that you'll actually contract it (unless you have some open wounds on your genitals). You almost have to have contact with an infected person's blood to get HIV and that's not something that happens everyday or even during sex (and a condom will pretty much eliminate those risks).
(I'm not a doctor, so this is all just AFAIK

).
There isn't always some easy fix to natural problems. Like other conspiracy theories, this one mainly fails in its assumption that people (or some group of people) have ultimate power. Nature is not easily controlled, it can kick our ass any day of the week.