Actually the root issue there predates temperance by a wide margin. The US governments primary revenue sources in the early days were tariffs and excise taxes, particularly taxes on alcohol.

Alcohol is a great commodity to tax because stills require lots of sugar, grain and barrels and thus are/were very easy to spot. Even today, the ATF will drop by for a visit if you're purchasing large quantities of sugar, and you'll have a hard time buying lots of sugar without identifying yourself.

Many states followed a similar model, so there is a historically ancient precedent of such regulation. Temperance and post-prohibition regulation added more layers.