They don't "run countries," but there is massive corruption.
Prohibition is basically a price-fixing scheme, and makes illegal drugs obscenely profitable. Years ago I knew a friend who got into it, and he made over $20,000 in one weekend by simply driving a car across the border once. (He ended up getting in trouble unfortunately, though he's much better now and no longer involved.)
If a person is willing to put up with the risk, there are few more profitable businesses.
I've heard recent figures around $400 billion per year globally. So you've probably got cartels that were they legitimate businesses would be on the Fortune 500.
With profits like that, large-scale operations have a lot of money to throw around to bribe cops, judges, government officials, etc. So as a result, the large cartels end up with a privileged position. Smaller operations that cannot afford to have such people on their payroll get targeted preferentially.
Look into the history of bootlegging in Chicago in the 20s. It's the same kind of thing.
The horrible thing about prohibition is that it's such a potent force for institutional corruption. The naiveté of the soccer moms that support it is disgusting. They all need to be beaten with a reality stick.