As an actor and occassional storyteller I find I sometimes have to inflect or put-on an accent. Singing a song is often done in the same vein. With some songs it would sound grating to be pronouncing a 'dialect' word in another accent and could spoil the reception. That doesn't mean you have to put on a whole accent where an inflection would do.

For example, a song like Anachee Gordon rhymes 'me' with 'dee'(do) and would sound absolutely bizarre if sung in, for example in a Black Country accent. With something like Burns, the rhyme may rly on a Scots pronunciation of a word which would be different from another reading (as has been discussed).

Personally, as a Scots/Geordie half-breed (born and brought up in the Midlands) who has travelled a bit, I often find my accent slipping into another when I speak to a person from, or even discuss topics relating to, a particular region. So if it happens that I sing songs with an inflection if it relates to a character of the narrator.

Funnily enough, I don't tend to sing songs like Black Velvet Band or songs from the former colonies (US, Australia... hee hee)with much, if any inflection. I don't know if this is because the (imaginary) narrator might well have been without an American or Australian accent themselves.

Regarding Blues, I wonder if it because many of the lyrics don't involve regional pronuciation that allows a singer the possibility of keeping their own accent.

If anyone ever wonders about singers toning down their accents, a quick blast of Juliet Turner will solve that one. Broad, unapologetic and all the better for it!