Gertrude Berg cagily kept her Molly Goldberg character on the air as long as possible. She started in 1929 with "The Rise of the Goldberg," when the plight of poor immigrants trying to live in a new country (specifically the urban East Coast) was certainly within memory of radio listeners. It was an era of dialect humour.
By the 1950s, television supplanted radio, ethnic humour was out, and the people were deserting urban homes for the suburbs. Berg felt Molly Goldberg and her husband Jake had to do the same. That's reflected in this promo for her series.
Berg tried one more time with the same character with a different name in a 1961 sitcom co-starring Sir Cedric Hardwicke. She was nominated for an Emmy, but the show was pulled after half a season on CBS; it was opposite "Hazel." Berg died in 1966.
Today, people cringe at almost any time of stereotype, but the Goldbergs were not over-the-top (certainly not compared to vaudeville acts), and were a welcome presence in American homes for more than 25 years.