I hadn't imagined a actual story, just a simulator/RPG with a beginning but no end. Even among RPGs with a story, the best run in a sandbox which you can wander around at will. Obviously only a limited number of venues, managers/agents, music publishers, etc can be made available, but how the player handles his or her career would be completely up to them.
I think allowing the player more custom say in their band would be better than slapping decorations on a story pre-fab. A set story runs the risk of 'this isn't who my character is'. Giving me some good emotion to look at in cut scenes (RB3)/ performance life (ala RB2) also added to the 'who this person is' instead of telling you outright 'this is how you are'. Nice to figure them out for myself.