Well, if you haven't made it legal /enough/ to actually allow for legal+public production and distribution, of course you're still going to have cartels. Who else is supposed to get people their drugs? If anything, it probably makes the cartels worse by increasing demand. It's incredibly stupid.
If you want to kill the cartels, you create a legal alternative, perhaps even government controlled (government is, for example, the only legal source of most booze here), and price it under whatever level the cartels need to turn a profit.
Of course, like the mob, this is most effective at stopping them from starting, not destroying them - that will take years, as they've undoubtedly diversified their business, and of course they can still make money shipping to other countries where things are questionably legal. So its no silver bullet, but it hurts them.
Making possession legal just fixes the half of the equation where you ruin families and lives to toss people in jail, it doesn't hurt the crimelords.
Once again, legalization of narcotic substances might not even make a dent in the profits of any drug cartel. Really, it might even increase their profits many-fold, depending on how savvy the guys in charge of them are.
And the safe bet is, they're very savvy.
Do you have any evidence of this? (And obviously, I'm talking in regards to legal competition i.e. legalized production, not just consumption)
Also, JoshuaFH, I just got to say - your arguments kind of infuriate me. It's pretty much the only reason I'm against nationalized healthcare - I'm terrified of giving it any more ammunition. And frankly I'd rather die in agony than live in the sort of dystopia your arguments conjure up, where individuals exist for the good of the state instead of vice versa.