Y'know, I don't disagree with you about musicals and operas - after all, is 'Die Fledermaus' an opera or a musical? Because it was written by Johann Strauss II, it's an opera but because Hammerstein was writing for the Broadway stage, 'Carousel' is a musical. Hmm.
It's a matter of perpective, I suppose. A composer called Krenek wrote a German theatre-piece called 'Jonny spielt auf' ('Johnny plays') in the mid-20th century which was conscioulsy not opera, but not musical either. Kurt Weill's theatre pieces also aren't operas, but why are they so different to Wagner?
Don't get me started!
Yeh, Gershwin's 'unknown' pieces were attempts in the 'classical' style, but then, much of Anton Bruckner's early symphonies are little known, but are still what would be called 'classical'.
The derivation of the word 'classical' is a whole different subject! Ultimately, we each like what we like - doesn't matter what it's called. I enjoy film music (the 20th century's big contribution to serious music) but it doesn't have to be classified as anything for it to be enjoyable.