That's a bit of an oversimplification. If the drugs they move are suddenly legalized, do you really think they're going to shrug their shoulders and drop everything? It might slow their imports here, but we aren't the only country who uses drugs, and you can bet the country where they're already hanging bloggers from overpasses won't be able to stop them from exerting control.
Mexico is a nexus of the drug trade not because they manufacture lots of drugs, but because they is infective law reinforcement and a porous border with the US. Consider West Virginia's largest crop by cash value is pot, but they have minimal drug related violence because it's highly decentralized and relatively far from major markets.
Pot cultivation went way up after 9/11 due to the increase in border security. It just isnt cost effective to smuggle a kilo of pot versus a kilo of coke. Pot is pretty difficult to move in large amounts so it make sense to grow it north of the border. Wholesale pot might go for 2-3k per key while coke might go for 10-20k per key.
I never said Mexico was a nexus of the drug trade. I said it currently has violent cartels running the show. You cannot point to West Virginia, who has no such history, as an indicator of what would happen in Mexico if drugs were legalized.