Why did Busby Berkeley stage dances no theater audience could see?

Because he wasn't making them for a theater: he was making them for a camera. Busby Berkeley's numbers typically begin on a stage, then grow beyond anything a real stage could hold, with dancers' bodies forming kaleidoscope-like patterns whose intended viewpoint is straight above. No seat in any theater is there; a camera can be. That is the film musical's great advantage over the stage: the biggest difference is usually lavish scenery and locations that would be impractical in a theater.

A musical film weaves songs, often with dancing, into its story, usually to advance the plot or develop a character, though sometimes a number is just an elaborate break. Berkeley, a choreographer known for elaborate set pieces featuring multiple showgirls, revived interest in the genre in 1933, and he brought an unusual influence to it: the drill precision he had experienced as a soldier in World War I.

The genre's popularity hasn't always been steady. In 1930 alone, Hollywood released more than 100 musical films; by 1931, oversaturation had set in so badly that only 14 came out, and studios scrambled to cut songs from films still in the pipeline—Life of the Party, originally shot as an all-color, all-talking musical, had its songs removed before release, and the same fate hit Fifty Million Frenchmen and Manhattan Parade, both filmed entirely in Technicolor. Because audiences had come to associate color specifically with musicals, the genre's sudden decline dragged color filmmaking itself down with it for a while, before The Wizard of Oz in 1939 became a landmark musical by experimenting with Technicolor.

The genre also let some actors escape their typecasting. James Cagney, a former stage singer and dancer stuck in tough-guy roles, won an Oscar for finally getting to sing and dance in Yankee Doodle Dandy, calling it one of his finest moments, while director Otto Preminger's Carmen Jones and Porgy and Bess starred Dorothy Dandridge, considered the first African American A-list film star. Musicals fell out of fashion again in the gritty, realism-obsessed 1970s, but they keep returning: Damien Chazelle's La La Land tied the record for most Academy Award nominations, with 14.