I love Ledger's performance but I don't find it very canon.
Well the whole objective of the Nolan films was to take these fantastical characters and move them into a more realistic setting, very similar to the original run of the ultimates.
Imo when you get to the essence of the Joker, he's a guy that realizes the entire world is insane. All the rules and hierarchies and the entire structure of it is insane, it's just organized insanity. We're all playing house in this world pretending to be rational and logical.
He loathes power structures and order, and sees reliance on them, and the belief that they keep you safe, as weakness.
The way he makes the criminals think they need to rely on him, that they are on the same team against authority, is classic joker. He doesn't want to operate as part of the counterculture within the system, or overthrow one system and replace it with another.
He wants to burn down all systems, eliminate all order, he's the ultimate anarchist. That's what the scene with him burning the money represented, the other criminals never saw him coming because he doesn't care about money or power.
The same with the scene with Michael Caine describing burning down the forest to get the guy they were after. When your enemy doesn't have rules, doesn't believe in honor or fairness or any rules of combat, you have to abandon your sense of honor too, and sink to their level to win.
The elements of the joker forming alliances and violently breaking them, and how do you beat the joker without becoming the joker, are strong themes in most of his major appearances in comics and the animated universe.