Mexico only has drug lords because US drug laws fuel their black market.

If you are skeptical of this, there are academic papers on the topic. You could also examine the history books regarding the rise of organized crime there. (For that matter, the rise of organized crime in the US was largely fueled by the prohibition of alcohol as far as I understand it.)

I am confused about what you mean. First, the federal government clearly has authority over international commerce. Second, the price of drugs in legal markets would be much lower, which would likely reduce revenue for criminal gangs in foreign lands. Third, the U.S.-Mexico border is long and it's hard to enforce smuggling laws, anyway. And fourth, Americans are quite capable of producing drugs on their own, and even more so if they were legal.

Cigarette smuggling is a thing because regulated cigarettes are more expensive than unregulated cigarettes. Why would that be any different for other drugs?

The revenue of bootleggers is sharply down since the 21st Amendment, because many people still choose to buy legal alcohol rather than moonshine.