Just a shower thought…
Can Obi’s:
“Then my friend is truly dead. Goodbye, Darth.”Be edited to:
“My friend is not dead. Goodbye, Darth”This can help to explain why Obi leaves and does not kill him. It will also explain Vader’s line of “Obi-Wan once thought as you do” in ROTJ.
There is no perfect answer. He tells Luke that Anakin is dead so the dialogue works there. Dialogue doesn’t need to explain Obi leaving, he does not because that’s who he is.