Illegal production of homebrewn alcohol is a thing and has been for centuries. Raising taxes at will does not mean that everyone will, unhappily, continue to buy expensive alcohol in the store. There is a limit after which people will start to produce their own moonshine, which is less safe than whatever you buy legally. Or start drinking various chemicals that resemble alcohol. (Window cleaner is a big hit.)
The problems with War on Drugs translate neatly to any possible War on Alcohol as well: the black market will kick in once it has a good business case to exist, and all sort of problems will come with its emergence.