What led the feds to put these three together?
One hell of a party?
ATF history page.
I just figured they wanted to lump all the cool stuff together.
dont forget Explosives
Alcohol and tobacco are obvious candidates to be joined. They were among the first items on which federal excise taxes were levied, and for a long time were just about the only items. As for firearms, the ATF site sums it up about as pithily as possible in a single sentence:
Maybe the “Bureau of Controversial Industries” would be a better title! Nah, then they’d have to include oil and porn.
Well, the porn could easily be lumped in to create the “Bureau for the Control of Really Cool Stuff”
Maybe based on a redneck night out? 
My ex worked for ATF. In the bureau, it was “affectionately” known as Booze, Butts, and Bang-Bangs.
If we want to stop skirting the truth, we could throw in porn and call it the Federal Nanny Agency.
Taxing these commodities sidesteps the question of whether the government has the power to ban their possession per se. Congress has the power to make laws to regulate interstate commerce and levy taxes - and in the process make life difficult and/or expensive for those who possess and trade these items.
Bryan’s link says ATF was split off in 1972 from IRS. Thus the term the moonshiners used for still-busting feds: “Revenooers.”
Fifty unlicensed fully-automatic assault rifles?!
NAUGHTY STOOL!
Taxes. Before the Supreme Court rolled over for FDR, the federal government used taxes to restrict and control things that it didn’t like. They didn’t prohibit the ownership of automatic weapons, they imposed heavy taxes and paperwork requirements. This was also done with drugs like marijuana.