I mean the in-story reason is he has no reason to kill him. Anakin in the flashback said mercy doesn’t defeat enemies vs defense of life. He was never chasing Anakin in this series.
Anakin is still fighting Obi-wan. Obi-wan is worried about Luke restoring balance. He only came out of retirement to save Leia.
Anakin acting like that dude still mad about a loss 20 years ago while you have moved on with a wife and kids. It just seems kinda pathetic.
Isn't the fact that Darth Vader is a psychopath who spends most of his time terrorizing the galaxy and murdering people a good enough reason?
Think of all the people Vader wouldn't have been able to murder over the next decade if Obi finished him.