Hi Rnm4 - I'm gonna have to call shenanigans on one comment you make, the one about the violinist and the tubist. Your story speaks more to the people involved, not the instruments they happen to play. A person is no more inherently musical because he plays the violin rather than the tuba. To argue otherwise is absurd.
That said, lets get to your legitimate points. Yes, some 20th century composers wrote symphonies, but they are not Classical in any sense (with the exception of course of Prokofiev's famous first symphony), including structurally. Wagner's influence on the composers that followed extended for many decades on music in general, not just opera (in fact, the development of opera did not at all happen as he envisioned it, a fact his detractors love to point out - this fact, however, does not diminish his actual influence on the history of music). Pretty much every composer after him had to deal with what he had done, either for it or against it, well into the 20th century (in great contrast to Beethoven, who everyone loved). Current, 21st century composers are free of this, of course. But there are many reasons why Wagner was as late as the 1980's the third most written about figure in the Western world, behind only Christ and Napoleon. Not sure if he still is, but as of his centennial in 1983 he was indeed. Some of these reasons don't have anything to do with music, but let's not get into all that here. Speaking of him as an artist, I still maintain that there has never been a greater iconoclast in the history of the arts. After Beethoven, music went in new directions, definitely, but after Wagner, it was never the same, splintering off in countless directions from the possibilities he opened up.
@Tubegroover - the above statement was exactly what Greenberg and I got into a great debate about when I was taking a seminar from him in grad school. I deliberately made it (during my required presentation, for which I had chosen Wagner) to bait him into that argument, just to see how much time I could get him to waste on it, because I knew he wouldn't be able to resist it. Who won? Take a wild guess, it was his class, and he had to keep control of it. But afterwards, he admitted being very impressed by my argument, which was really nice of him to say, and he didn't penalize me for the wasted time, either. I did like him alot and I do highly recommend his stuff - he has a great way of presenting things in very clear ways to musical laymen.