People say "what about Raiders?" but those films were not really advertising the 1930s. Once they got into the desert or jungle it could have been present day. There wasn't much to identify it as the 1930s.
"Nobody loves a fat man except his grocer and his tailor."
Indiana Jones movies are full on amusing nods to older adventure stories, serial movies and such but the scripts were written in a way that audiences don't need to get these things since there are also other things to enjoy, like their sense of humor, which is not really of any particular time period.
I definitely didn't "get" what Lucas & Spielberg were doing with these movies when I was younger - they were just exciting adventure stories. Now that I've grown to know & love older movies and literature I like Indys in a completely different way. However The Rocketeer for example relies more heavily on audiences' interest in particular era and its popular culture, which is why it didn't sell.
I guess the only ways to write oldies / pulp fiction scripts and make them into commercially successful movies these days would have to be either making them obviously ironic / comedies, or sneaking these themes in as spices and not as the main course.