In the case of the Gold Diggers and Broadway Melody series, you forgot the original films in the series: Gold Diggers of Broadway (1929- Only two surviving reels), and The Broadway Melody (1929- The first musical to win Best Picture).
Basically, it’s a way of reminding people that 1) These films are connected to each other (albeit mostly by the producing studio- Warner Bros. made the *Gold Diggers * movies, MGM the *Broadway Melody * series), and 2) To distinguish the films in the series from each other.
There had been annual stage production reviews on Broadway, etc., before that. Such shows would sometimes have a year designation in order to let people know that a new version had come out. In carrying over to the movies, the stage show became the backdrop of the story. Once movies killed this stage show genre, people stopped caring, etc.
What ftg said. Those reviews were dated (not meaning old, but that they had dates with them) also. You had the Ziegfield Folies of 1921 and the Scandals of 1923 etc. They were labled so you knew you were getting the newest version. As was said, this numbering of the review carried over to the flickers.
It started on Broadway in 1907 with the Ziegfeld Follies, which was followed by annual productions through most of the 1920, each containing the year in its title: Ziegfeld Follies of 1908, etc.
Another series began in 1919 with George White’s Scandals and its sequels George White’s Scandals of 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1928, 1929, and 1931.