"Seemingly" in that if two make sense under a specific philosophical idea, one always seems forced in (Example: prohibition covers alcohol and guns, but tobacco?). What was the logic behind this?
Taxes.
Here is a good history already typed out: http://www.reddit.com/r/AskHistorians/comments/1g8543/why_does_the_atf_and_dea_exist_as_separate/caiuraf
In short, the ATF was not formed in the interest of public safety, it was formed for tax collection. Even up until the 1970s the written mission of the ATF stated: "The principal function of the Enforcement program is to prevent the fraudulent non-payment of taxes which results of the traffic in illicit liquor by the criminal community."
Even though the mission has evolved slightly, there is still the common thread that the three things you listed are subject to excise taxes. Federally regulated firearm "permits" are actually tax stamps.