Drug criminals and users are often associated with high crime and violent activity. Therefore, the War on Drugs will in essence help reduce overall crime and violence too if it is successful. Eliminating drug crimes and sales when possibly will dampen the criminal activity that these drug users were often doing before. Not to mention it will decrease illegal drug sales which is a crime too.
In almost every study on the matter, branching through miles of statistics the war on drugs is an utter failure. It has increased our private prison system, bankrupted the state in many areas, and imprisoned countless non-violent offenders for the sake of limiting the choice of the american people to make their own decisions.
Many studies show it doesn't even cut down on drug use so how would it cut down on violence? There would be no need for violence in a legally regulated system.