Yeah, up to a point.
The problem is that comic writers kept trying to outdo one another and shock their audience.
Joker kidnaps an heiress so he can steal the crown jewels? Just throw him in jail and stop him next time!
Joker beats your sidekick to death with a crowbar? Ok, it's personal but it's just one murder, can't sink to his level.
Joker shoots the police commissioner's daughter through the spine? Gordon wants to show that the law works so bring him in without killing him.
This all makes sense.
Now, though, you've got Joker murdering hundreds of people on a whim and Batman does nothing. "We have to rehabilitate him!" Yeah Bruce, the guy dressed like a nightmare clown who murders people is gonna be fine with some group therapy.