Generally you can recognize a person by their voice. This means that almost everyone has an accent. Therefore, if you only sing in your 'own' accent then you are pretty much limited to songs that you have written yourself.

I come from The East End of London but I don't speak with a broad Cockney accent. Would I, or would I not allowed to sing Cockney songs, if I can't affect an accent when I sing?

And how far do we go if we have to Anglicize (or Welshicize, or whatevericize) our songs? Should Geordies have to Geordyize any non Geordy song that they sing?

Should nobody but Londoners be allowed to sing 'Streets of London'?

Gawd the few hundred songs in my song list would be reduced to a few Dozen.

As Dick says - 'whatever works'.