The underlying issue do not suddenly disappear when you legalize drugs.

That’s technically correct, even though “underlying issue” here should be plural because addiction is multifaceted.

But I think no one is arguing that in the first place, the argument is that decriminalization has to be a part of the plan.

From the article:

decriminalising drugs leads to a substantial drop in substance abuse and addiction rates. Countless studies have shown this.

The issues do not disappear, but you lessen the stigma of addiction, and allow for official support, thus making the issues more manageable.

Given true choice, most people will avoid the highly addicting substances. Removing the stigma, more people will get help. Sort of an immediate, double-benefit on ending addiction issues