TDK Joker's motivations are clear, The Joker literally explains why he does what he does, the only thing they don't explain is his past. There's layers that you seem to have missed. Leaving his background a mystery in TDK is intentional, not an oversight. He's written as the ideological opposite of Batman and the line about the world burning is to show Batman that he couldn't handle Joker the way he has others because he doesn't have typical motivations which is what Batman needed to understand because he couldn't figure him out.
You're comparing a character study to a film featuring a fully fledged character, it's like comparing an apple to a grapefruit and saying it's a shitty fruit because it's not tart enough. Or, for a more specific example, complaining that the first Star Wars sucked because we don't know everything about Vader's past.
The problem I have with this Joker is that he's painted as a down on his luck sympathetic character. Any iteration of the Joker I've seen shows him as a highly competent albeit disturbed individual but he isn't even hinted at as highly competent in this movie even after he starts coming into his own, which, no matter how disturbed, that intelligence doesn't simply develop, it should have already been there and we should've seen shades of it. I needed to believe at the end that this was the beginning of a mastermind who could challenge Batman, what I got was a fairly average mentally ill guy who snapped and wanted people to stop being meanie heads to him. That doesn't work for me, especially after the brilliance that was TDK. If it does for you, that's fine, your enjoyment of the movie doesn't hurt my feelers.