Fincher and co. adapted the book again. It's sort of like a new version of a play; new actors, new director, new sets etc. but the text remains the same.
Sometimes people want to adapt a book (or a film) because they like something about it (they keep "that" but dump the rest) and sometimes because they like a LOT about it. I think Fincher really liked the book.
I don't think it would've been a good idea to give him a fake accent. It doesn't make a lot of sense that everybody is speaking with an accent, anyway, I mean, these are Swedish people in Sweden, aren't they? They wouldn't be talking English with a Swedish accent to each other, they'd be talking Swedish - interpreted as English in the movie for our viewing comfort. So I don't think it'd make more sense to have Craig speaking with an accent, because the accent is not part of the world of the film and the characters. I can understand that it makes for a weird contrast, though.
I've said it before, it doesn't bug me at all, as long as the accent sounds right and not fake.
Movies are inherently artificial and having an audience hear "English" when the characters are speaking something else is just another example of that artificiality. This, and many other things, are handled by conventions that have evolved over a hundred hears or so of cinema and even longer in other forms, especially literature.
The regional accent idea is interesting, but when Oliver Stone made his Macedonians Irish in 'Alexander', was that really less distracting than fake Greek would've been? Or the actors using their own voices?