Batman Begins was not realistic. Not even "to some degree". It's no more realistic than B'89. But it's the way in which the movie was presented that allowed you to suspend your disbelief. A Microwave Emitter? Would have fried the innards any human being within a mile. Batman attaching himself to the train? His arms would have been torn from their sockets (no matter how much "armor" was on his little rubber-clad body.) A grappling gun? No way anything that small could shoot a cable of the required thickness with such force, let alone be able to hold up a 200 lb. man.
The thing was, with all of these, what got you to believe them was the world and context it was set in. Because the world you saw looked believable, the things within it didn't seem so far-fetched.
Also, for the movie's most improbable of devices, they provided short, semi-scientific, "I'm going to use big words so it sounds like I know what I'm talking about" explanations. These were, of course, mostly BS, but the context in which they were presented allowed you to believe them.
I don't see why the same can't apply with permawhite. Give us a permawhite, adapted to the gritty context of the movie. Have a character who seems like he knows what he's talking about give a short, shadowy, vaguely- scientific "explanation" of the Joker's appearance. I guarentee you, you wouldn't have a single complaint.
That's really the thing with people who say permawhite doesn't work in "Nolan's vision"; had "Nolan's vision" included permawhite, no one would have said a word. In fact, you would probably be hearing things like "Nolan was a genius for having brought permawhite into the real world!"