There is a line in Tim Burtons 1989 incarnation of Batman where Batman tells Joker “I made you, you made me first”. This is one of the clearest examples in movies of how the characters need each other. Without an adversary, they are just mad men in costumes, they give each other purpose, and giver the films a narrative. Jack Napier as the person who killed Bruce Wayne’s parents, then later became the Joker is an invention of the Movie. The symbiotic nature of the Batman/Joker relationship is perfect; as is the Heath Ledger incarnation in The Dark Knight (2008). We don’t know the origin of this version of the character, he tells just appears fully formed as a character. At various points in the film, Joke tells different, conflicting stories about the scars on his face. When arrested, Gordon describes what they know about him, nothing! “No matches on prints, DNA, dental. Clothing is custom, no labels. Nothing in his pockets but knives and lint. No name. No other alias.”
By the this point, there are so many Joker origin stories, who knows what is or isn’t canon. In his comic books, the character was created in the 1940’s by Bill Finger, Bob Kane, and Jerry Robinson (who is mainly responsible has been disputed). Starting life as a criminal mastermind, intended for a single issue, he became a mainstay. As the Comics Code Authority came into effect in the 1950’s be became less of a psychopath, and more of a prankster, before returning to darker roots in the 70’s and 80’s. The idea of Joker as a failed comedian came from Alan Moore’s seminal The Killing Joke (2008).
The One thing, they all have in common, is Batman. Even when Joke is the focus of the story, his nemesis Batman is there, until now! This new incarnation director Todd Phillips (who co-wrote the screenplay with Scott Silver), is Batman free, we do see a young Bruce Wayne, and yet another death of Thomas and Martha Wayne, but no man dressed as a bat. This is cleary a story without Batman, and it wouldn’t work with Batman. Joker would be a different character, and the film would be very different with Batman. The Martin Scorsese inspiration is clear, particularly Taxi Driver (1976), and The King of Comedy (1983), this gives a more gritty reality than we have ever seen in a movie of this type, even Christopher Nolan’s trilogy. The echoes of Rupert Pupkin we see it the character of Arthur Fleck are emphasised by the inclusion of Robert De Niro who appears in Joker in what is essentially the Jerry Lewis role from The King of Comedy.
By the time I had seen the film, it had something of a critical rollercoaster; winning the Golden Lion and Graffetta d’Oro Venice Film Festival, and a series of four and five star reviews were followed by a backlash of its portrayal of mental illness, and a sympathetic portrayal of a homicidal maniac. There was then a backlash against the backlash. Whatever your thoughts on the film, there are two things that are hard to argue: Joaquin Phoenix is fantastic as Arthur Fleck, and the score by Hildur Guðnadóttir is sensational. Ultimately I think the film is really good, but not excellent, I can’t help thinking those who love it are blinded by how different it is to a typical DC movie, and those that don’t like it are concerned by the controversy, or sniffy about its comic book origins. 
As to the question, Can there be a Joker without Batman? that is something history will tell us. The film is intended as a standalone story. As this it works, and as a viewer, we can see a world in which a character like Batman could exist, we are seeing a cities decent into the crime ridden place we have seen in other Batman movies. We see Jokers decent into madness, and his total disconnection with reality, but we don’t see a fully formed criminal mastermind. This is where it needs to be left, lefty for the viewers imagination. If however, the studio decide to catch in (at the time of publishing the world Box-office had topped $770million) it will dilute the story and have a negative impact on the original film. Indications they are that Warner Bros intend leave Joker as a single film, but will “launch DC Black” a series standalone films with a darker tone, based on DC Comics but not related to the DCEU. To put it another way, Joker as a character can work without Batman, but the film Joker can ONLY work without Batman, and not as a precurser to a Batman Movie.
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