'A traditional singer has to sing traditional songs' (Dick)
I'll argue with that any time you like, Dick. A traditional singer can and does sing what the hell he/she likes.
I will also argue on any grounds that certain Music Hall songs have become traditional songs under any valid definition of traditional song. Where would you put Sharp's 'The Jolly Wagoner'? (One example among thousands)
Where would you place the bulk of broadside ballads that have become traditional songs? (95% of the songs in the Sharp/Hammond/Gardiner/Kidson/Baring Gould etc Collections)