While there are some awesome Batman villains, I agree.
None of them have the dynamic the Joker does. The Joker is like the complete opposite of Batman. Chaotic, maniac, big smile, kills without a second thought.
All the Joker tries to prove is that anyone, no matter how just they think they are, no matter how steadfast they believe themselves to be, are only a single bad day away from turning into a monster like him.
He wants to push Batman over the edge, because Batman is the biggest challenge in that regard. If he can bend Batman, he can bend anyone. So if he can get Batman to kill him, his point is proven.