It's called a "finaletto."
I would say Rossini either invented it, or it was a common device in 17th- and 18th-century opera and he did it more than anyone else. (Mozart tended to end his first acts better than Rossini.)
Gershwin used finalettos ("finaletti"?) throughout the 1920s in his musical comedies and then in the 30s in his more sophisticated musicals like Strike Up the Band. Other 1920s musicals had one too, like No, No Nanette. Jerome Kern and Kurt Weill used them too.
There's even one on Broadway now: The first act of How to Succeed ends with a song Frank Loesser actually called "Finaletto."
I'm not a Viennese operetta expert, but I think it was a common way to end a first or second act (when there were three acts). It makes sense when you think of it: the big choral sound is exciting.
That's part of what was revolutionary about West Side: You have this orgasmic quintet, the audience applauds, they think they're going out on a high, and wham! It's a choreographed fight scene that leave two of the main characters dead and the male lead a murderer. Intermission!