I disagree about Green Day just slapping their songs together and calling it a musical- from the start, "American Idiot" had a plot and told a story (with 21st Century Breakdown being an examination in closer detail of basically the same story from a different angle), and on stage it told that same plot and story.
Whether it was a good story, or told well, is an entirely different question, and one that there appears to have been no final consensus on.