Usually taxes such as these are proposed to address some external costs. But the problem with making the leap from a beer tax to alcohol and drug abuse (and related crime and treatment) is that this is an external cost only associated with a small minority of beer drinkers. In fact as I mentioned in my earlier post, moderate beer consumption may actually cause a positive externality, suggesting (economically) government may wish to subsidize moderate consumption.
Other taxes are different. Take a gas tax, there is a large and recognized cost associated with the release of carbon into the atmosphere and it doesn't matter how much you drive, when you drive or how fuel efficient your car is - the carbon content of a gallon of gas is the carbon content of a gallon of gas. When you consume a gallon of gas in any manner of use, the cost to society is the same. Thus a tax on gas is purely Pigovian. We all pay a price that reflects the costs we impose on society.
Not all sin taxes are like beer taxes, the effect of cigarette smoke are harmful for even moderate smokers and also for those around them. So a tax is much more efficient in addressing the external costs here. But Beer is simply not the same thing. As a occasional and very moderate drinker of beer I impose no external costs - so making me pay a higher price is not Pigovian but simply an arbitrary, and distorting, tax.