I find the whole business of vocal styles and accents quite interesting. Endlessly interesting, in fact, because you can argue it forever and whatever "rule" you come up with you will find exceptions too.
Singing in your native accent.... well that's a risky game. Some accents more so than others. Singing in an English folk style is generally not a good career move. People tend to run screaming from that stuff. Even, for some reason, the English who seem to love everybody's folk music but their own.
I have always enjoyed bands that sung about South African things and like South Africans - though, of course, there is no one "South African" accent. Particular examples of this were James Phillips and a fab 80s band The Genuines. They had very different accents as James was a white boy from Springs (and sang like one) and The Genuines were coloureds from Cape Flats (and sang as if they were). I liked the way that Jennifer Ferguson would incorporate local slang into her lyrics (I still think she must be the only person to make the Radio 5 play lists with a song that included the word "larnie"). I even recall a hip-hop band from Cape Town, Prophets of the City who I liked a lot because they rapped with Cape Flats accents about life in the Cape Flats.
All of that is great from an artistic point of view and for people who enjoy local colour, but it may not get your music onto MTV.
An awful lot of vocal styles are contrived. Whoever it is is trying to sing like somebody else. Sometimes it goes beyond just being influenced by your influences and is more deliberate - EG Bob Dylan (who made lots of money) and Martin Carthy (who didn't).
But there's no rule that I can see. Some regional accents seem to be impediments to a career, and some don't. A Jamaican accent never seemed to reduce anybody's prospects.
Famous contrived vocal style: Sting.
We might wonder at the target of these words from a recent Richard Thompson song. The song's title is "Geordie" (Sting is a Geordie). Thompson says it's a song about somebody who was very rude to a good friend of his but he'll say no more for fear of law suits. But that doesn't stop us wondering....
Come now Geordie, sing us all a song!
Whoah there Geordie! Where's your mother tongue?
That don't sound like Tyneside to me
Geordie are you from Jamai-kee?
Though you can go too far with that sort of purist attitude and end up like the British folk movment in the 50s where there were expectations that Scots had to sing Scottish songs in Scottish accents, in the interests of "authenticity". Scots could only sing Scottish songs and Londoners had to sing like Londoners and leave songs from Yorkshire alone etc etc. It had a point in that it challenged the performers to locate and embrace the traditions of their native region, but it got out of hand. And, besides, songs don't always respect boundaries.
The whole issue of authenticity in popular music is pretty moot, and has been at least since a whole bunch of English white boys decided that they were going to sound and play like American Negroes from the Mississippi delta or Chicago.
Just about EVERYTHING about Mick Jagger is contrived and Keef's guitar playing owes fairly obvious debts to Chuck Berry and Ry Cooder, but is that sufficient reason to not enjoy the Stones?