Here's my PoV - feel free to shoot at anything you don't agree with.

"Traditional" describes what happens to a song once it is released into the wild, not where it originally came from.

"Anonymous", "old" and "traditional" are not interchangeable terms: a song can be any combination, all or none of these. Songs of unknown authorship are "anonymous". They may have been written yesterday or 500 years ago.

If there is a tradition of singing a particluar song, it may be regarded as "traditional", totally irrespective of whether the author is known or not. If the song has been in some way altered by this process we are on firmer ground in regarding it as "traditional"