An interesting discussion, and revealing to me in terms of one specific composer: Richard Wagner. I think I saw Wagner’s name mentioned once, as a "candidate" for inclusion in the top five. Nobody dared to put him on their list.
Which is odd. Everyone with an interest in music of any kind should at least read a review of Wagnerism, Alex Ross’s vast 2020 book (it runs over 750 pages!) This isn’t a biography or analysis of the German composer’s music but an investigation of his influence on most intellectual aspects of human existence. Not just Art, of course—the subtitle of Ross’s book is "Art and Politics in the Shadow of Music." But an astounding array of great non-musicans including writers, poets, visual artists, dancers, filmmakers, and architects all incorporated Wagner’s approach to creating their own work. And they all regarded him highly not because of some theoretical "advance" he was responsible for but because of the effect Wagner’s music had on them. So, Friedrich Nietzsche, Thomas Mann, James Joyce, WEB Du Bois, Theodor Herzl, Willa Cather, Isadora Duncan, JRR Tolkein, Anselm Kiefer, dozens of film composers, and so many others were all committed Wagnerians.
But though the operas are as popular as ever onstage and on recordings, Wagnerism has declined sharply since the 1940s, thanks to an association with totalitarianism that won’t be vanishing soon, if ever. Listeners are less likely to admit to loving his music, which is as intoxicating as Tchaikovsky, as lyrical as Schubert, as dramatic as Beethoven, and as spiritual as Bach for fear that it marks them as a fascist or bigot. The fact that Wagner’s music continues to powerfully endure despite all its "baggage", even if it’s no longer a kind of religion, tells us something.