There was supposedly an alternate ending
In a recent episode of Kevin Smith’s Fatman on Batman podcast (around the 16:35 mark), the filmmaker cited “somebody who works in the business, they’re in the know, fucking super smart, and a great storyteller” telling him about an alternate ending to Joker that never came to fruition. The final scene still happened in the mental hospital, but instead of killing the psychiatrist, Fleck laughs to himself after telling the story. The doctor would have asked why he was laughing, to which Arthur would have said, “I was just thinking of something funny.”
Suddenly, the film would flash back to the murder of Thomas and Martha Wayne, this time at the hands of Arthur Fleck. As usual, Bruce Wayne is left crying next to his dead parents. But as Arthur walks away from the scene of the crime, he would stop, look back, shrug, and shoot Bruce Wayne. Cut to credits.