He made Similar arguments have been said about beethoven, Liszt, Wagner etc
However the fact is avantgarde as a term did not exist in the time period and it is really a 20th century construct used to retrospectively apply to artist who were original in the past.
My argument is that the cutting edge composer of the 20th century aka the serialist are fundamentally different to the cutting edge composer of the 19th century and earlier. Originality prior to schoenberg was originality within th context of music as entertainment. As Greenberg even said himself schoenberg 12 tone technique revolution invented a new language completely different o the entire history of western musix and the 12 tone technique was responsible for the alienation of classical music from the audience (this is from someone who actually liked schoenberg). He also emphasis that schoenberg 12 tone technique works will always sound modern and shocking because it is in a different music language to humanity while other composers of the past may well be shocking at their time but eventually became part of the music furniture. He Predicts that the ultraserialist work of the likes of Boulez, stockhausen etc will never be part of the music furniture due to how intrinsically alien it is. The Avantgarde cutting edge of the 20th century has no completely accurate parralels to the past
So while yes you can draw some similarities/parralels between cutting edge composers of the 20th century to the past (which was what greeenberg was saying when he is calling them Avantgarde artist). They are fundamentally different artist. I don't believe the same terminology should retrospectively used to describe pre 20th century artist and from my knowledge it's not academically accepted to classified cutting edge artist of the past as avantgarde either