The Joker is the essence of the Antithesis of Batman and is his equal. Batman will not kill him because he is not like him and Joker won't kill him because he strives for to have Batman break his moral code. they are two side of the same coin that the Batman is incorruptible and the Joker is irredeemable.
There’s something about Batman and Joker’s dynamic that Origins just gets right imo, maybe it’s the thrill of their first meeting, how much and how fast it changes them, and watching them seem to realize the potential that they could do this forever. Either way this game is up there as one of my favourite representations of them :D
The Reason Batman can't kill the Joker is because a lot of people ask why doesn't Batman kill? and the canon answer is that you're gonna get from Bruce is that "if I cross that line where do I stop? or if I cross that line. the number of killers remain the same." that's what Bruce says and that's what he convinces himself of. but I think the answer is actually a lot more complicated than that. if you make someone who has encountered Death at a very early age. because trauma forms and sticks in your mind very easily that the younger you are. so when Bruce encounters death at 8 years old. he has this trauma that's deeply imprinted in his brain and trauma can lead us to do different things. it leads an alcoholic to drink and it leads a narcissist to obsess about themselves but in Bruce's case he has a pathological obsession that is a compulsion to preserve life at all costs. because Bruce couldn't kill anyone if he tried because if you put a gun in his hand the same way that if you put a bottle in an alcoholic's hand. they're gonna drink and if you put a gun in Bruce's hand he physically can't pull the trigger because he has this mental block against taking someone's life and he is compelled to preserve life at all costs. that's what his trauma did to him and that's why he physically and psychologically cannot kill.
I think part of how Troy Baker's Joker manages to be distinct from Mark Hamill's is that Hamill's Joker is someone skilled at putting up a persona, who cracks enough jokes that you forget he's willing to put you through the worst pain imaginable (which makes his colder turns all the more chilling, like in Batman Beyond). Baker's Joker has that humorous persona blend with the murderous intent from the outset, with a younger disposition that makes him so much more excitable and dangerous (also MUCH fruitier). You enter a room with that Joker, you know you're not leaving alive. Hamill's Joker fits best with the Arkham series as a divergent continuation of the 90s show (Asylum and City). Baker's Joker fits best with the Arkham series when it tries to tell its own origin stories and do its own thing (Origins and Shadows). There's also the benefit of Origins coming right after City, so we have a performance of a Joker trying everything in his power to keep on living fresh in our minds as we experience a performance of a Joker with absolutely nothing to lose.
''Pfft, I'm over my BatJokes phase, time to move on to other gay nonsense'' The Lord Shen comp literally leading me to this masterpiece: ''Well, shite''