What if you were a Mexican drug lord and one day you wake up and the millions of acres of crop that help sustain your empire are no longer profitable? Seems like that would reduce crime to me.
The only reason black market anything exists is because the government doesn't understand supply and demand. If you keep raising the price above its market value via taxes, of course the free market economy will adjust itself and you will start seeing the mafia peddling cigarettes and booze again. They'll undercut the government, factor in the risk involved, and still come out making a profit. The blame for this lies squarely at the government's feet.
Not very convincing....if you think the mexican drug lord is just going to roll over you're dilusional. Since he's a criminal already does it not occur to you that he will engage in some other criminal behavior.