The 1954 definition seems a pretty good basis to me, though obviously it's not written in stone and brought down from the mountain. SA's efforts however are circular and carry no information, so appear useless to me as an analytical tool.
The 1954 text attempts to define characteristics of one vast body of music which appears to be somewhat different from other vast bodies of music in the world. It uses the word "folk" when it refers to that body of music. I find that quite a useful thing; it is in no way helped by lots of other people trying to use the same term "folk" to apply to their own particular favourite type of music which does not share the chacteristics referred to in the 1954 (attempted) definition. The category then becomes so broad as to be useful. To those people I would say (as did Bert Lloyd), invent a new word for your new all-embracing category.
To me, many of the various versions of the Wild Rover I have heard are a product of a folk tradition. Lady Gaga's Bad Romance, Richard Thompson's Beeswing and Beethoven's 6th, are not products of a folk tradition.(though of course variants of any these might become so). So I find the distinction usefu, and, where not useful, interesting.
Others, of course, may not.