I saw the first film and thought 'Well, it's well made and well acted, but so what? He's not the real Joker.' He's more like the guy who inspired the true Joker to rise decades later. He would be an old man by the time Bruce is trained and ready.
You can have different interpretations of the mythos, I get it. But one crucial thing is Joker's stance that he's not really insane; that something happened to him in his past that convinced him the world was insane instead, so the only true answer is anarchy and chaos. It's the source of his battle of wills with Batman, that people are inherently bad and anyone can fall.
Giving him a mental illness that he needs medication for in Joker, it's a crutch that changes things too much the wrong way.