The Joker wasn't the first time Heath Ledger had come into contact with Christopher Nolan or Batman. When the then-up-and-coming director's total restart of the Caped Crusader was still in pre-production, Ledger was approached to play Bruce Wayne, but turned it down in pretty resolute terms, quoted as saying, "I would never take a part in a superhero film."
That could be exaggeration on Nolan's part, but it's not inconceivable rising star Ledger would want to keep out of the super hero circuit. Remember that this was a time when the genre had only a couple of respectable contemporary entries (X-Men and Spider-Man were the only notable hits) and the franchise itself was still marred by the all round failure of Batman & Robin. Taking on an important part of such a film would at best see you forever typecast in genre films, at worst completely kill your career.
The film that changed all that was Batman Begins, a grown-up, realistic take that used its funny page-originated characters to explore real-world issues and relatable emotions. Beating the likes of Robert Downey, Jr. and Samuel L. Jackson to the bandwagon, Heath Ledger contacted Nolan cold about playing the Joker in the sequel shortly after the movie hit.
Obviously that turned out magically, but there's still fun to be had thinking how Ledger would have done Bats. Just imagine how even more psychotically wounded Bruce Wayne could have looked.