Yea, it’s always been weird to me that Batman alone is being judged for not using lethal force.

Batman is the focus of the narrative and the audience. Of course he will be the focus of the criticism. But technically yes, a lot of others in universe do also share responsibility for any further victims of the Joker. After a certain number of escape, spree, capture, escape, spree, etc cycles surely they must have realized he cannot be rehabilitated and will continue the remorseless mass killings until he dies.

or even proximity to him, be morally obligated to kill him?

This is a compelling idea for sure, and could definitely lead to interesting questions in other cases. Let's say the Joker has a body count of at least 1000 victims, how far back do you have to walk that number before such an obligation is no longer reasonable. Would a serial killer with 40 victims also be such a clear and present danger that they'd represent a moral imperative for their elimination? Or does it have to reach comic book levels of obscene?