Of course alcohol is a drug.
It seems then that a black market in a drug is an entirely apt comparison, after all.
However, when any reasonable person says to another reasonable person, I want to go take some drugs, what would immediately come to mind? A shot of vodka? I think not.
You're right, I don't think of alcohol, or nicotine, or caffeine, even though I know these things are drugs. I also don't think of marijuana. Marijuana, like the legal drugs, is common enough (and, I'll say it, mainstream enough) that we ordinarily call it by its own name, as distinct from other less popular activities. That's why we call marijuana and the legal drugs "soft", as opposed to other drugs which are called "hard". If we're going to follow common usage, why not that distinction? But we should remember that at least some hard drugs are only hard because they're chemically purified -- if we permitted the coca leaf and coca tea, it would be no different from permitting coffee beans and coffee.