See, this is a rather simplistic and ignorant comment. I do not mean to insult you - actually, I wish it was as simple as you're saying, just kill them and end with it. However, the problem is incredibly more complex than what you think it is.

I live in Mexico, next to a city that a couple of years back was one of the worst in the country in terms of violence and drug distribution. (In fact, one of the big cartels started in that city.) I've interacted with people involved in those cartels and with their families. I've interacted with officers who're in it, too. The problem is deeply rooted, and it's a problem of, among other things, culture.

The solution is not to "kill them all," but rather to educate. According to one article[1] (note: it's in spanish), Mexico invests less than 0.5% of its GDP into science and research. While Mexico has always had top competitors in international competitions for math, biology, robotics, science and engineering in general, and even chess, they're anomalies and products of extremely expensive private schools. Hell, even GNOME was made by two Mexican hackers. Schools in Mexico are beyond messed up.

Lack of education, mixed with poverty, create criminals. In Mexico you rarely ever see racism, but instead there's classism. Unlike in the US, our government officials aren't old white guys, but people of all kinds of skin color with money. Mexican culture - and maybe I'm wrong in this comparison, but this is from what I understand - is similar to black culture, where you have to fight your way out of your impoverished group by primarily violent means. You don't earn the respect of your fellow poor friends by getting an A on a test, but by having designer jeans or by having the latest iPhone.

And this is what gets most the "bunch of degenerate shitbags that have been given firearms" that you mention. These are literally teenagers (or even younger kids) that want to get out, probably even help our their family or community, and this is the only way they can do it.

I may be going a bit off-topic, but killing them off won't do any good. In fact, starting an all-out war might make things worse. These kids don't fear death because they have nothing to lose. The higher ups also don't fear the government or the army.

Another thing is that, if a war against organized crime were to start, it would create fear instead of peace. It would make the population, at least to my understanding, "uneasy" to say the least.

What I would propose instead of killing people would be to educate and invest in shit other than fighting a meaningless war.

[1] http://www.metronoticias.com.mx/nota.cgi?id=378883

EDIT: Hmm, I noticed that I rambled a bit too much. There are several other things I wanted to mention. I am not in a position to offer a concrete solution as I'm not an expert in this topic. I've only seen this from afar and read almost daily on the newspapers about what's happening in the country. As I mentioned, the problem is far too big to be reduced into a couple of paragraphs. There are countless books, articles, essays, blog posts, etc, devoted to this specific topic and the solution offered varies (albeit slightly) from person to person.

If anyone is interested in more information, let me know and I'll see what I can do.