"It feels like in a world where people were generally interested in solving the issues with the drug trade the DEA wouldn't need to exist."
Drug prohibition has never really been about solving the problems society faces with drugs. In the early days when cocaine and heroin were first made illegal, the argument was overtly racist. Black cocaine users would be more accurate with a gun, would go into a frenzied state where they attack white women, and would be difficult to stop even when shot in the chest. Philipino immigrants were bringing their bad opium habits with them, and heroin was marketed by a German company. Marijuana was said to cause white women to want to have sex with black men, and good white boys were being corrupted by Mexicans who gave them marijuana.
In this day and age the war on drugs is not overtly racist (but it just happens to disproportionately affect black communities -- coincidence, really!), but we now have a host of new reasons for it. Drugs are an easy way to terrify a population that grew up with war on drugs propaganda, and politicians looking for a few more votes can easily play up their "tough on crime" stance with drugs. Deploying soldiers to arrest suspected drug dealers is the norm, and police forces wanted to build a paramilitary wing can always turn to drug crime as a justification for it. Pharmaceutical companies love the war on drugs because it inflates the demand for prescription medications; a prominent example is methamphetamine, the supposed scourge that also happens to be prescribed as a treatment for narcolepsy, obesity, and ADHD (you can bet that the pharmaceutical grade methamphetamine is cleaner and purer than the stuff you buy at a truck stop). Alcohol and tobacco companies lobby in favor of the war on drugs (ironically), for obvious reasons.
So really, to understand the war on drugs you just need to change your perspective. Do not think in terms of solving the problems associated with drugs, because that is little more than a facade. Think in terms of money and power, which are the real purpose of the war on drugs and the reason we will not see the DEA disbanded any time soon.