This usage of "should have" appears to be a Britishism. I wonder if anyone cares to provide an explanation of the British "should have" usages.
Several observers have emphasised Dusty Miller's devotion to the Joyita and reported his insistence that the boat was unsinkable. Why, then, would he willingly have abandoned ship under any circumstances? According to Robin Maugham, Charles Marsack said, "I can't imagine why he should have left her. And I don't believe he did." (source: Joyita: Solving the Mystery 2002)
The passage deals with MV Joyita's 1955 disappearance. Miller clearly is believed to have abandoned the boat, so "should have left" here does not indicate a wish contrary to what happened in the past, rather, a confirmation of what happened. Why "should have left"? What sense of should is invoked? Here's another similar sentence:
What puzzles me is why he should have left without telling me. (source: Cambridge Dictionary)