I don't know why I hadn't seen Roman Scandals, even though I like Eddie Cantor and Busby Berkeley, and Berkeley was at his peak when Warners loaned him back to Goldwyn to do this film (he'd been the choreographer on the stage and film version of Cantor's Whoopee!). The "Keep Young and Beautiful" number is on YouTube, and it may now be the most famous part of the movie because it's the most appalling: not only is it Cantor's obligatory blackface number, but the whole song is about how women (including a young Lucille Ball) should spend all their time trying to be impossibly thin, wrinkle-free and perfect if they "want to be loved."
It's a great Harry Warren tune, though, and Al Dubin's contributions to these musicals are underrated: in numbers like this and "Shanghai Lil," he wrote a huge number of additional lyrics covering any idea Berkeley had. Because of Dubin, these were musical numbers that really used the songs to advance their own little self-contained stories, instead of just having Berkeley illustrate a short pop song.
The strange thing about the number is that as it progresses and gets more and more surreal and bizarre -- the usual pattern of a Berkeley number -- it almost seems to be rebelling against itself. First it betrays one of the rules of a blackface number by having the dancers actually notice that Cantor is a white guy in blackface, and get quite angry at him for it. Then the two groups of dancers, black and white, who were originally separated from each other, join together and team up against their common enemy: Cantor, the white guy pretending to be black, the man telling them all how they should look. They use one of the beauty treatments they had to go through to "keep young and beautiful" as an instrument of torture against Cantor, pumping their fists in revolutionary style.
I doubt Berkeley actually intended this to be some kind of act of revolution against the traditional blackface number or girlie number. But he would follow his crazy ideas wherever they took him, and that's where this particular idea seems to take him: the chorus girls take over the number, stage a coup, and kill the star.