Markets change. Once upon a time it was booze and guns, now it's drugs and guns. If there hadn't been a market for cocaine, the Taliban wouldn't have been able equip themselves with more than sharpened sticks. If there hadn't been a market in the US (US/ Mexican border) and Europe (Spanish harbours) for drugs, the likes of Escobar and later Gallardo wouldn't have been as influential as they were. Gallardo especially left a bit of a legacy creating most of the current Mexican drug cartels (based on the same principle as the internet really, if one got busted he would still have the others). Of course, since they cut off the head, the cartels became completely autonomous and started fighting amongst themselves. You need to do two things to eliminate them though, you both to deprive them of their markets and their arms dealers. So far, Texan arms dealers alone seems to be able to provide them enough guns to wage a military style campaign against government forces.
In theory, you could go after the distribution networks, but so many people are involved and so many palms greased that it is futile prospect. Take the buyers out of the equation and money for guns and corrupt officials dries out, or as in Nepenthe's example of self styled "revolutionaries", they can't buy PR and public opinion. Then, when no longer all powerful in the minds of people, you can realistically wage a campaign against them.
You're being a bit TOO hip talking about the Texans. Texan arm dealers aren't the ones supplying the cartels with heavy machine guns and RPGs. Kit being used regularly against regular Mexican armed forces. There may be semi-autos etc coming from Texas, but cut off the easy route and you can bet your ass they'll find another source. Either from within the mlitary or from elswhere on the drug supply chain. Colombia, Peru.
Eliminating the demand for drugs is surely an even bigger fantasy than one might come up with ON drugs. Demand is a part of what we are as human beings. It's tied to things like depression, and involvement in gangs and vice. But tackling those things is something which could take generations. Certainly at least one generation. What happens in the mean time?