Will he be “deeply missed”? Well, not by dissidents, Shiites, non-Muslims, protestors in neighboring countries ... and for everyone else, only by comparison with the incompetence or chaos or still greater cruelty that might come next.

But Americans should feel some limited sympathy for the late king, because our relationship with his kingdom has something in common with his own. Like so many despots, Abdullah was to some extent a prisoner of the system he inherited, interested in reform in theory but unable to find the room or take the risks required to see it through. And we in the United States are prisoners as well: handcuffed to Saudi Arabia, bound to its corruptions and repression, with no immediate possibility of escape.

Much of America’s post-Cold War policy-making in the Middle East can be understood as a search for a way to slip those cuffs. Three consecutive presidents have tried to reshape the region so that alliances with despotic regimes will no longer seem so inevitable or necessary. And all of them have failed.

For Bill Clinton, solving the Israeli-Palestinian conflict was supposed to be the catalyst — in ways never quite elucidated — for reform and progress in the wider Arab world. For George W. Bush, or at least his ambitious advisers, the invasion of Iraq was supposed to create a brilliant alternative to our Saudi alliance — a new special Middle Eastern relationship, but with an oil-producing liberal democracy this time.

For President Obama, there have been multiple ideas for how we might, as an administration official put it during our Libya campaign, “realign our interests and our values.” The president has tried rhetorical outreach to transcend (or at least obscure) our coziness with tyrants; he tried, in Libya and haltingly in Egypt, to put his administration on the side of the Arab Spring; he and Mr. Kerry have made efforts to restart the Israeli-Palestinian peace process; he has sought some kind of realigning deal with that other font of cruelty, the Islamic Republic of Iran.