I get the "savouring the sound and feel of the words" - but I regard that as something of a guilty pleasure: the native-speaker is not "savouring", etc., when singing the dialect song, so when you or I are savouring, we're play-acting, rather than allowing the song its own life, so to speak. My own rule of thumb is to bring a dialect-song (if I must sing it) as close to my own natural pronunciation as I can manage. Sometimes the way a word or phrase is set to the melody requires a bit of an exaggerated or affected twist, but I try to minimize these.

OTOH, there are children of immigrants who say they grew up singing songs with the full-on accent of their parents, so that seems to be the natural way for them to sing ... so ... I don't know. And once I had an elderly Scottish woman adamant that I should sing "Ye'll tak the high road" rather than "Ye'll take", the way I'd learned it on my mother's knee (I've compromised ever since with something half-way between a long and short 'a').