Leveller, "the Tradition" is a shorthand term, jargon if you like, for the shared transmission and evolution of music amongst a community over a period of time. There are many other traditions, but it should be perfectly obvious which one we are discussing here.

As for it existing, there is not only plenty of evidence for its previous existence, but there are still places where it continues.

If you don't like the word, feel free to suggest an alternative, but to deny its very existence in the face of all the evidence seems perverse.