Even though MGM made the first real movie musical, The Broadway Melody, in 1929, and even though that film was a huge success, the studio spent the rest of the 1930s playing catch-up with other studios as far as musicals went.
Like the rest of Hollywood, MGM was taken by surprise when the musical fell suddenly out of favor with audiences in 1931, and that year it abandoned a big musical shot in two-strip Technicolor partway into production. The musical form was revived in 1933 with the movies made at Warners featuring the surreal production numbers of Busby Berkeley, and it was given further impetus by the Astaire-Rogers films made at RKO, but MGM struggled to find a house style or a house franchise to compete with those of its rival studios.
It capitalized on the name of its first big musical hit, and the film's popular title song, with a series of Broadway Melody musicals, starting with The Broadway Melody Of 1936. It made the musical super-production The Great Ziegfeld in 1936, which was a big critical and commercial hit but didn't really establish a franchise, though the studio later produced a couple of films, Ziegfeld Girl and Ziegfeld Follies, whose titles and content referenced the earlier blockbuster.
MGM did create a somewhat specialized musical franchise in the form of operettas during the 1930s, many of them starring Jeanette MacDonald and Nelson Eddy. These were enormously popular films but operettas had essentially played themselves out with audiences by the end of the 1930s. Attempts to revive the form with Mario Lanza in the late 40s and early 50s met with mixed success.
Eleanor Powell was the studio's big conventional musical star throughout the 1930s, though her magical brand of tapping wasn't really suited to romantic pas de deux. She thus never became part of a signature dance team, being usually paired up with the studio's up-and-coming, non-musical leading men, like Robert Taylor and Jimmy Stewart. She had other limitations as a musical star. She wasn't a great singer -- her vocals were almost always dubbed -- and she didn't have great range as an actress. She made one film featuring some magical dance numbers with Fred Astaire, The Broadway Melody of 1940, but for some reason the two were never teamed up again and the film became the last of the Broadway Melody series. Another was planned, to star Powell and Gene Kelly, but it was never made. After that, MGM seemed to lose interest in Powell.
At about the same time it also lost interest in Lucille Ball, whom it had hired away from RKO and tried to establish as a musical leading lady. Ball was a better actress than Powell, with a very appealing screen persona, but she wasn't a great singer, either, and her dance skills were limited to those of an accomplished chorus girl, which is how she'd started out in show business.
One reason for the neglect of both these ladies was the rise of Judy Garland as a star. After her wonderful performance in The Wizard Of Oz, Arthur Freed, making his debut as a producer, teamed her up with Mickey Rooney in a series of musicals that went through the roof at the box office. Finally MGM had a showcase franchise, based on a boffo musical-romantic team, that almost instantly vaulted MGM into the forefront as a producer of movie musicals. Before that franchise could play itself out, Freed, always looking ahead, had begun casting Garland in more mature roles without Rooney, inaugurating a series of superior and radically innovative musicals that left those of the other studios in the dust.
From here on out the rest of Hollywood was destined to play catch-up with MGM, and the Freed Unit, on the musical front.