> why do they persist with it? A few reasons present themselves
Also: theatre.
Much like a lot of airport/airline security measures are theatre to reassure the common people that something is being done, the war on drugs continues because people who don't know any better (or don't believe the ineffectiveness argument) will feel less safe if it officially stops or even steps down a notch. This situation perpetuates itself, and any escalation doesn't get reversed, and feeds into the politics point others have already mentioned because people feeling less safe are less likely to vote for you next time.
Also: theatre.
Much like a lot of airport/airline security measures are theatre to reassure the common people that something is being done, the war on drugs continues because people who don't know any better (or don't believe the ineffectiveness argument) will feel less safe if it officially stops or even steps down a notch. This situation perpetuates itself, and any escalation doesn't get reversed, and feeds into the politics point others have already mentioned because people feeling less safe are less likely to vote for you next time.