This is an important observation, which I second not merely because I used to argue it strenuously with another member who is no longer on the forum. Wagner is as insistent a tonalist as Mozart, which accords with his tribute to the latter, calling him a "great chromaticist." Wagner didn't want or try to get out of tonality, but to see how much could be got out of it. His last work, Parsifal, is in its extremes of both diatonicism and chromaticism a tribute to the tradition of tonal harmony, as well as an extension of it, much as his Meistersinger is a tribute to the contrapuntal tradition of Bach.Old post, but I feel compelled to note that atonality was basically the antithesis of Wagner's aesthetic style that involved the tension created by the ambiguous, androgynous suggestion/co-existence of multiple possible keys and tonalities. The profound, impassioned yearning in much of Parsifal and in the opening theme/motif of Tristan is built from that tension. Atonality eliminated this tension by eliminating tonality altogether. You can't have tension without tonal hierarchies and the expectations those tonal relations create. Atonality, despite what some may say (including the atonal theorists) was not a logical progression from Wagner's ambiguous tonalities, it was a complete destruction of everything Wagner himself tried to achieve with his tonal innovations.
In the basic elements of his musical vocabulary, Wagner was more summation than innovation, and yet the effect of much of his work was of something unprecedented and challenging. That effect came not only from his unprecedented emphasis on chromaticism, but from his breaking down of familiar formal templates in favor of an apparently free expressive narrative allied to theatrical action, which replaced the more or less closed forms of traditional arias and ensembles - "apparently free," because the narrative was given coherence by carefully plotted key relationships and the elaborate deployment of interrelated and interacting thematic germs (leitmotifs). The choice to illuminate the dramatic action of the play in this way also entailed the extension of music's time scale, not merely in the length of his operas (there had been other operas of similar length) but in the rate at which musical ideas are introduced and disposed of. The "story" of a sonata movement may be told in ten minutes, but the "real life" pace of theatrical action allows for a more leisurely exposition of musical ideas which have the new function of tracing the shifting psychological states of the characters, as well as commenting on the larger context of the drama, even on things absent, things past, and things to come. It's no accident that the title of Proust's magnum opus, "In Search of Lost Time" (commonly known in English as "Remembrance of Things Past") was invented by one of many writers inspired by Wagner's musical meta-narratives.
I do think it's fair to say that Wagner played a major role in "revolutionizing" modern music. The unmooring of music from traditional forms in favor of an apparently free expressive narrativity was an important innovation, but it was one that less masterful composers followed at their peril. Wagner himself warned against applying his ideas in the context of non-operatic works, saying once that "in the symphony one thinks very differently." His statement of intent to write symphonies after Parsifal remains one of music's tantalizing "what ifs."