It does the movie industry a whole lot of good to keep in mind that cinema is all about experimentation. Unfortunately, both Hollywood filmmakers and their audiences (that's us, by the way) seem to have become rather comfortable with the existing forms and styles of cinema, and experiments aren't always very welcome.
Moulin Rouge is, more or less, experimental cinema. It is the kind that does not fit into any of those inevitable classifications, namely action, drama, adventure, romance, comedy, musical… tempted as I might be to call it a romantic musical, I won't because ....