You bring up a valid point, Apple.... that story allowed us (the audience) to get some background information, but using that same argument, by Michael insisting that Kay listen to Fontaine sing it allowed the movie-makers to add some "entertainment" to the movie (the music).
Michael told that story with some sort of "pride" which belied his feelings about the Family. This wasn't unusual for him.....he'd later try to show that he was dealing with his feelings because it was business, not personal. But we know better.