I don't think any of the legalization crowd thinks it will fix problems with heavy drug use. It's that it will stop wasting tax money on a useless War against them that isn't working.
For example, I see it as being a choice with 2 options. In Option A, people still ruin their lives (as people will always do) and it's illegal so we spend 80+ billion a year to fight it and fail.
In Option B, people still ruin their lives, but we don't spend 80+ billion a year trying to stop them from doing so. Or for you big government folks, we spend 80 billion a year trying to help them (not imo a good idea, but better than a failed war)
I see the second option as a better choice. This is another argument like guns that pulls in a lot of emotional arguments that aren't based on facts though, so it's hard to talk about it.