There is a parallel between Organized Crime and the movie industry. Organized Crime was one of the ways for social climbing, of getting out of poverty and ethnic matters.
In the main Hollywood studios, many directors were ethnics: Samuel Goldwyn and Louis Mayer (M.G.M. studios: Metro Goldwyn Mayer), David O. Selznick, Charles Chaplin…
The cinema was a new technology founded by the elite, the ethnic entrepreneurs and the W.A.S.P. businessmen. Some innovative sections of business were opened for the same reason (legitimate, profitable). These people found a renovation of the American Dream either in Organized Crime or in cinema.
Producers did not push gangster films for the simple reason that it was not that popular at the time. They gave the public what they wanted (and the WASPs were rather conservative). It is only when it generalized that gangster movies “took off”.
Another connection: several actors became movie stars because of their ethnic origins: James Cagney was Irish. (Public Enemy), Paul Muni was (Scarface)…
They brought the ethnic accent to the screen. They would have never been movie stars in classic films. It is thanks to the gangster movies and to the parallel made with Organized Crime.