"Classical music may have fallen out of popularity, but film music in the classical style is certainly popular."

That's true, same with musicals, but it's a great shame that many more people don't listen to say Mozart/Da Ponte's Don Giovanni and Bach's B minor Mass. Those works are a part of the great musical canon and two of the greatest works of musical art ever to come out of the Western Tradition, and if people were given the right opportunity and environment I believe many, many more people would appreciate them. Moreover, whilst I'm unashamedly biased in saying that, I've even heard learned musicologists echo similar sentiments about those works.

I selected two examples I love but I could have chosen other very accessible classical works such as Magnificat BWV 243, and the The Marriage of Figaro. or other equally famous ones.

Sure, opera has fallen out of favor, but if given half a chance I'd defy modern audiences not to like Don Giovanni. As you'd know, even if one doesn't speak Italian, once one understands its synopsis one is compulsorily drawn in by its drama—which is the equal of many a modern work—sex, rape, murder, a macho he-man who's often the secret envy of many men, an uninvited ghostly figure who comes to supper and demands the villain's repentance and his refusal to give it, then his inevitable descent into Hades—and all that to WAM's divine music. Even today, drama doesn't get much more intense. The Don was such a scandal in 1786 in that it was banned in Vienna and first performed in Prague.

Similarly, there are many other works that ought to be easily accessible to modern audiences but they seem to be only appreciated by the small cognoscenti, Die Zauberflöte for instance.

You refer to certain classical works or excerpts as being still popular and I'd agree, but I'd make the point that as far as general popularity goes they are the vestiges of a past era. No doubt these works will remain popular but that they are mainly excerpts shows that most modern audiences have little tolerance for the remainder of such works, or the patience to investigate them further and deeper. One sees this trend even on FM stations dedicated to classical music, instead of playing the full work they'll play an excerpt. Frankly, I find just hearing Dies Irae alone and apart from Requiem somewhat annoying, the context, mood and setting are lost by not hearing the complete work. Carmina Burana is a wonderful work so why wouldn't someone want to hear all of it? Incidentally, have you seen or heard the modern interpretation of Carmen called The Car Men? I once caught it by accident on TV and was mightily impressed.

I understand the reason for excerpts and the popularity of works such as Eine kleine Nachtmusik, they don't require much effort to appreciate and these days people are overloaded with information and activities and have little time to listen and digest the more complex parts of a work. Moreover, that's not always easy and it often takes considerable time to develop one's full appreciation. I use myself as an example, when I was a kid and young teenager, I'd listen, say, to Beethoven symphonies and love them, but it wasn't until my 20s that Schubert's lieder like Die schöne Müllerin, and Winterreise, had the power to reduce me to tears.