BrE usage of "should have"

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)

The sentence I can't imagine why he should have left her expresses a personal judgement or reaction to a behaviour.

In the entry on should in Practical English Usage (page 512) Swan states in the section titled reactions: It's surprising that she should...:

Should is also used in subordinate clauses after words expressing personal judgements and reactions, especially to facts which are already known or already mentioned. (This use is more common in British than American English. It is not particularly formal.)

Swan gives the examples:

• It's surprising that she should say that to you.
• I'm sorry you should think I did it on purpose.
• Do you think it's normal that the child should be so tired.

He concludes:

In American English, would is more usual in this kind of sentence: - It was natural that they would want him to go to a good school. (BrE...that they should...)

The Wikipedia article contains the following: A friend of Miller, Captain S. B. Brown, was convinced that Miller would never have left Joyita alive.

Apparently Miller (and everyone else) was missing from the vessel, but there was speculation that he might have been injured and fallen overboard, or that the occupants had been captured. So his leaving voluntarily is not a certainty.

The use of should or would implies that the speaker cannot imagine a scenario in which it is probable that Miller deliberately abandoned ship.