I rather think that it's not singers with a distictive accent that's the problem, nor singers who are not using their usual launguage. For me it's the fact that when a stlye gets popular so many other singers suddenly take it up with variable results. Some get away with it but many don't.
Just had a wonderful thought. Wouldn't it be something if the funny accents of the Three Tenors singing in English became popular. We could all do it in the folk clubs. Make a nice change. Three Tenors wouldn't mind. They're famous enough to take it. Going off to practice right now. Joy