One the one hand you’ve got the real life realities of Darth Vader is in the other movies so he can’t kill him. But that’s obvious and not really the issue we’re discussing.
Back on Mustafar, Obi-Wan was ready to kill Anakin. In fact, he thought he did kill Anakin. And now that the two are fighting again, we get the sense this fight starts the same way. Obi-Wan is ready to end him. By the end though, we see a crucial manifestation of Obi-Wan’s conscious. He’s less inclined to kill “Darth Vader” than he is “Anakin” and since Vader says he’s killed Anakin, Obi-Wan sort of sees that as sad win.
And yet, this is a crucial mistake. Obi-Wan has no problems killing Sith. He’ll kill Darth Maul again in a few years time, this time for good. But his sympathy for the tragedy of Anakin Skywalker here results in an inability to finish the job and, as a result, doom the lives of billions, especially if you think about Alderaan. So we know why he didn’t kill him, but that was a mistake.