While this sounds like a terrific idea, I don't think it will work.
Your first scenario is not permissible (the "Do it" part is proscribed); a cop can't have sex to make an arrest, nor could the department legally require officers to have sex as part of their job.
The second scenario is plausible except that you assume that the LEOs have as much or more "firepower" than the gangs. In fact some kinds of crime pay so well that law enforcement is way over their heads trying to fight back. Maybe not so bad as what's going on in Mexico but bad enough. For example, http://www.rand.org/pubs/research_briefs/RB9770.html suggests that the combined spending on the four drugs {marijuana, cocaine, heroin, methamphetamine} is about $100 billion USD per year; more than half that figure remains even if you remove marijuana from the list. Compare that to the total federal law enforcement budget of about $28 billion https://www.whitehouse.gov/sites/default/files/omb/budget/fy2012/assets/justice.pdf which covers the whole gamut of criminality, not just drug sales. OK, stop the "war on drugs" and the cost will drop to zero. Organized crime (gangs) will just move on to a different lucrative area, whatever brings in the cash.
New York City's police budget, according to http://en.wikipedia.org/wiki/New_York_City_Police_Department is $4.8 billion and it covers everything from jaywalking to terrorist bombers. Police Commissioner Bratton can't even get the mayor to hire an additional 1,000 cops because the money just isn't in the budget.
Furthermore, LEO has to "play by the rules" when going after criminals; the gangs don't have to play fair, so they don't have to waste their resources doing things that don't benefit their illegal activities.
It would make a cool movie though :-)