Yeah when Batman sees killing Joker as just as bad as him murdering random Innocent civilians of Gotham, he's stupid.

Same for Two Face and Scarecrow and all the others. Batman by leaving people to escape jail and murder more each time is not helping Gotham.

I can understand Batman and his motivations, but I think he has blood on his hands, and not just from the crooks he leaves with crippling medical debt.

I am blaming Batman for his choice and for his reasoning.
He pulls the trigger, Joker (a psycho who's killed dozens/hundreds already and will kill even more) dies.
He doesn't pull the trigger, 3-4 innocent people die now and Joker goes on to kill scores more.

I argue Batman can't just wash his hands of responsibility because he CHOSE to put himself in that position. He decided to be the one with a motorcycle cannon pointed at Joker's face. If he didn't want to be responsible for life and death, he should have stayed home and gotten a massage. But no, he chose to be the city's defender, so there he is.

Perhaps it helps to drop the movie and pick another analogy. Imagine there's a mass shooter psycho walking around shooting children, and there's a police officer with weapon drawn and pointed at the psycho. Police officer decides not to shoot the psycho because his conscience says he doesn't want to kill anybody. And because he doesn't take the shot, the psycho kills 3-4 more kids.
Do you argue the officer is blameless for those childrens' deaths?

But Batman is ok with killing the henchmen of joker and other villains by dozens