What Is It About the 30's Pulp Genre?
I think it depends a bit on specifically where you're placing it and what you're looking to get from it, but in short, it's a liminal period in time and setting - it's the gateway between the modern(ish) period of WW2 and afterwards, but still with elements which belong to a much older age.
In that juncture, that flexibility gives both advantages and disadvantages - you can include modern sensibilities alongside the legacy of the Victorian and Edwardian eras and it still fits - there's enough romanticism and myth still alive to have a supernatural game but enough modernism that you can have a slice of life setting which is relatively accessable to people who don't know the period.
I think part of the reason it's perhaps not given as much love on its own is that it's a bit of a problem decade compared to the 20s and 40s - it's the decade of the Depression, the dustbowl, the slow emergence from the Crash, and the rise of fascism and anti-semitism, and the spectre of WW2 lurks heavily in the air above it.
In terms of the 20s, you've got a combination of post war optimism and social change, combined with the rise of gangsterism and increasing concerns about equality etc - it's also evocative in terms of Gatsby, Capone etc - it's a good setting for social games or action ones in the crime genre, and that's why most pulp tends to be set here rather than in the 30s, where everything is a bit more subdued.
In terms of the 40s, you've got the war, and everything that comes with it, so everything from early Hellboy to Band of Brothers, and again space for social games behind the lines in a kind of Foyle's War setting. After that, you can play around with alternative histories, or simply indulge in a pre-Cold War paranoia.
Comparatively, there's not a lot of really evocative material from the 30s which is exactly good for roleplaying - you've got Steinbeck and Hemingway, but most of that is quite depressing, no one's really having a nice time and it's very gritty and hyper-realistic. In terms of actual events, most of it is bubbling away waiting to erupt in the 40s.