Yup I agree, when I said "not to say Kid doesn't care if Killer gets hurt" I meant like I'm not saying Kid doesn't care, because he does.
But it's simply a nerf for Zoro because, several times in the rooftop fight Luffy has been caught in situations where he needs to be saved from peril (which Cinera already laid out), and Zoro has been so on point, he is sending attacks, doing real damage, and protecting his captain back.
Unfortunately, it also leaves him more susceptible to hits from Yonkou, causes him to spend energy and more time to saving the captain, than just focusing on taking down Kaido, like the others are just focused on.