In the old zombie movies there's often a debate on whether or not to kill the zombies. Because in the earlier zombie movies there is discussion on whether zombies can be cured or not. If there is a possibiliy for a cure, then isn't killing them wrong?
Especially in cases where zombies are not lethally injured but simply turn into a zombie by a single bite, this is a question that should be taken into consideration before killing them.
There's a musical called Zombie Prom that my school did a couple of years back, which had a similar plot. A boy committed suicide by jumping into a nuclear plant, and then when he came back as a zombie he realized how much he actually wanted to live, and tried to re-enroll in school, but his principal wouldn't let him because she didn't like him while he was alive. Then there were protests held by students to help get him back to school.
So it would be like Independence Day where when the aliens came and there were people trying to protest that humans needed to make peace with them while standing on top of a large building... until the aliens blew the f*ck out of that building and they all died.
Especially in cases where zombies are not lethally injured but simply turn into a zombie by a single bite, this is a question that should be taken into consideration before killing them.