I didn't read everyone's responses, so perhaps this has already been said. But, I think this is why doctors aren't talking about this:
In college, I became a raging alcoholic (I hadn't quite admitted this to myself). For depression, I then went on Celexa, an antidepressant. Within a week days, my intake of alcohol had dropped at least a quarter. Even more shocking, within just a few hours of my first celexa, I remember calling my sister and reporting how it was weird I was no longer craving alcohol. ( I later learned antidepressants work right away on anxiety, although they take a while to work on depression). But, then, over the years, my alcoholism slowly grew, and grew, and grew, until it was back and worse than ever. So, I think doctors are not talking about the medication you mentioned because it is not a cure. Alcoholism is progressive, end of story. I think mental health medication may, however, slow (but not stop) that progression. I don't know, of course. I'm just talking from my personal experience.