Each case is unique. There is no rule about this matter. If the singer sings the song in a way that is effective and compelling for the audience, then the singer is singing the song "well".

And it's a matter of individual opinion whether that is happening or not.

A lot of people love Tom Waites. I find him very hard to listen to. So hard that I barely do listen to him.

A lot of people love Bob Dylan. Others find him very hard to listen to. I find him very easy to listen to, and love the way he sings.

So it's strictly a matter of personal taste and opinion.

My opinion is, Bob Dylan often sang exceedingly well until quite recently. I'm not sure about Tom Waites. I don't know his material well enough to be able to make any accurate assessment about it.