Do “sin taxes” work?

TLDR: yes, they do (to some extent).

Particularly if they're not so high as to effect a "ban", the effect is a ban on people less affluent than some mark making "sinful" purchases in a particular jurisdiction. Sin taxes are particularly regressive, since they tend to be higher than typical sales taxes (which are already regressive in some sense).

Of course, as far as governments are concerned whether such taxes reduce "sinful" activities is irrelevant, so long as they increase tax revenue and allow politicians a way to improve their public images.

What if there was solid data decisively showing that there were substantial externalities effectively being paid for by the public? The answer to that, is that the power to determine this is too dangerous.

There do have to be rules and conventions, or there would be chaos. Since such power is dangerous, the exercise of it should be kept to a minimum. Then the question arises as to what that minimum is.

Before the federal income tax was instituted, the alcohol tax was the U.S. government’s single largest source of tax revenue.

The imposition of a federal income tax was the single most necessary goal for prohibitionists to push for the constitutional amendment for alcohol prohibition.

It’s also worth mentioning that during the time that the federal alcohol tax was active (created under the Lincoln Administration to help pay for the Civil War), Americans drank twice per capita the amount we drink today, so it didn’t even dissuade drinking all that much.

Americans were ferociously drunk in the 19th and early 20th century. Some historians argue that prohibition ended the era of the largely men-only saloons, and when women and men drank together in speakeasies, men tended to drink less, thus reducing overall alcohol consumption in the post-prohibition era.