Help with research: The 1930s War on Crime

I've got an idea for a TL, based on the idea that J Edgar Hoover is dismissed early on in Roosevelt's Presidency, and the Kansas City Massacre never occurs either because it's butterflied away by Hoover's dismissal or just a matter of altered timings meaning the assassins arrive late and Nash and his escorts aren't killed. Anyway, the removal of these two things prevents the Bureau of Investigation from emerging as the primary federal crime investigation organisation. I have a notion that this is in a world where Roosevelt was killed by Giuseppe Zangara as well, so no (or a much reduced) New Deal means the Depression and the Dust Bowl continue and the impetus for a federal police force disappears. This means that bank robbers like the Dillinger Gang continue to operate unchecked by federal authorities.

But I feel I don't know enough about how American law enforcement works. What were the powers of the Bureau? Were there alternative organisations that could have stepped into the breach? And there are other questions I'm probably not asking that I should be, which will occur to people better informed than myself.

So, what do you think?
 
A book: Public Enemies (2004) by Bryan Burroughs. Formed the basis for Micheal Mann's mediocre film of the same name, with Depp & Bale. Forget the movie - the book is very good, a history of the "FBI's War on Crime which lasted from 1933 to 1936, a period that saw the rise & fall of six major criminal factions: those of John Dillinger, Baby Face Nelson, Pretty Boy Floyd, the Barker-Karpis Gang, Machine Gun Kelly, and Bonnie and Clyde" (Penguin ed xii).

Burroughs profited from the release of FBI files on the period - about a million pages of reports, statements, etc; they detail amazing bungling & incompetence, and a slow learning curve until the FBI became the FBI. Terrific, should be the basis of any research you do.
Maybe the U.S. Marshals could be expanded to step into the Bureau's nationwide role?

Another great book, this time a novel: Elmore Leonard's The Hot Kid, a 1930s era tale about Carl(os) Webster, a US Marshall who is a sort of ur-Raylan Givens. Dillinger et al make cameos. Webster reappears in Up In Honey's Room, and short story collection Comfort To The Enemy.
 
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