There's no question that The Joker is one of the most iconic comic book villains of all time. The character has been portrayed numerous different times in countless different ways since his first battle with The Caped Crusader in Batman #1 back in 1940, and each portrayal has evolved him in some form or another. Jared Leto is the current go-to in the DCEU, but there's already more of the Clown Prince of Crime on the way.
Joker's Existence Is A Direct Response To Batman
First and foremost, it needs to be reiterated that Batman's presence in Gotham City has traditionally invited the more outlandish and flamboyant villains that he fights on the streets. In his first year as a vigilante, the Caped Crusader typically faced off against standard mobsters like Carmine Falcone; then The Joker showed up on the scene. As seen in films like The Dark Knight, as well as classic graphic novels like The Dark Knight Returns (in which The Clown falls into a catatonic state when Batman retires), Joker's very reason for existence is his never-ending quest to get a laugh out of The Bat. Even in Batman: The Animated Series, Mark Hamill's Joker falls into a deep depression when he believes that Batman has been killed and utters the somber lamentation, "Without Batman, crime has no punchline."
Joker's Origins Are Often Tied To Batman
There is no "right" way to do a Joker origin story (mainly because the character has never truly received a definitive origin story), but the various incarnations of the character almost always have one thing in common: Batman and/or Bruce Wayne was somehow involved in his creation. It could be the fact that Joker actually killed Batman's parents (a la Tim Burton's Batman), Batman failed to save him from a vat of chemicals (a la The Killing Joke) or Joker was originally the member of a gang who fought Batman (a la Zero Year). In the same way that Joker is a direct response to Batman's presence in Gotham City, when he DOES receive an origin story, it almost always relates to Batman in some form or another in order to give his obsession with the black-clad hero some logical basis.
Joker's Worldview Directly Contrasts With Batman's
Perhaps Heath Ledger's Joker said it best in The Dark Knight when he described his battle with The Caped Crusader: "This is what happens when an unstoppable force meets an immovable object." The reason they work so well together is the fact that Batman's sense of justice and his absolute refusal to kill directly contrasts with Joker's nihilistic sense that the world is utterly devoid of meaning. A story focusing on a battle between Joker and a more traditional anti-hero isn't interesting because there are no moral stakes, and sending The Joker up against a cop like Jim Gordon ends (in most cases) with Jim trying to kill him. Joker is an ideological threat, not a physical one. He needs someone to contrast his bright colors and dark sensibilities in order to work as well as he does.
Batman Doesn't Need To Be A Main Character In The Film
This is one thing that often falls through the cracks when people discuss a story featuring Batman and The Joker: both of them do not need to headline the story. Brian Azzarello's 2008 graphic novel Joker epitomizes this idea perfectly, as it offers a pure, unaltered Joker story that keeps Batman at arm's length for the bulk of the narrative. However, after Joker has encountered every single one of Gotham City's worst rogues on his quest to rebuild his criminal empire, he finally comes face to face with his polar opposite in one of the book's shortest (but most important) sequences. So what does this tell us? The Joker solo movie doesn't need to be a long story chronicling another battle between The Bat and The Clown, but it does need to acknowledge their relationship and dynamic in a meaningful way.