Ben won’t kill Vader because he still considers Anakin his friend, he wants him to grow & gain the wisdom that Ben knows he’s capable of learning.
I see that lackluster writing is still being patched by fans with assumptions never sustained by anything in the actual show…
The only reason Ben doesn’t kill Vader is because Vader needs to be alive at this point of the lore. That’s the only reason. Anything else is only fan theories that the tvshow makers never thought about giving or implying any kind of explanation 👀