This obsession with "realism" has got to be toned down. Especially when dealing with a concept like Batman. Batman may be more realistic than most superheroes, but that's not saying much. If you are unable to suspend your disbelief for some of the mythology's elements, how do you suspend your disbelief for the character the mythology revolves around?
Permawhite skin is not an impossible concept. It is possible for people to bleach themselves, as evidenced by Michael Jackson. You can color your skin via plastic surgery, tattoing, or even skin dye, and it can be somewhat permanent.
Now, permawhite from a chemical bath may be a bit more absurd, but when you look at the kinds of things chemicals can do to skin or other material...it's just not that farfetched a concept.
Nolan used makeup. He chose to do so instead of using permawhite, just as he chose to use segmented armor instead of something a little more subtle. It's simply his choice, there is "This is why it HAS to be used in THIS franchise" argument that anyone can make. It is simply down to personal taste and a filmmaker's choice. This is a concept that any reasonable person should realize. That both "concepts" of The Joker's appearance can be rationalized in a fairly realistic manner.
The makeup is just that, makeup. It's used not because Nolan wanted to use something more realistic than permawhite, but because he felt The Joker should wear makeup. Odds are there is a reason for this, and I would imagine it's the metaphor behind it.
I like the idea of The Joker being permawhite with no explanation, or even via the chemicals. I like the idea of The Joker wearing makeup. I don't like the actual visuals they have chosen to employ in THE DARK KNIGHT. It just screams of a design team that needed The Joker to look "extreme" and couldn't be subtle about it on any level.