After I wrote this post, I had an email conversation with John Cooper of the history faculty at UW/Madison, who wrote the New York Times article to which I was reacting.
Cooper points out that the shadow cabinet concept has been applied in the U.S. He told me that Thomas Dewey, the unsuccessful Republican presidential nominee in 1944 and 1948 "designated John Foster Dulles as his point man on foreign policy, and he was privy to what was going on. [Secretary of State George] Marshall took Dulles with him to the conference that hammered out NATO, and the European foreign ministers greeted him as the next secretary of state."
Most observers expected Dewey to defeat Harry Truman in the 1948 presidential election. But Truman won and, as Cooper puts it, Dulles "had to wait for another four years".
When Dwight Eisenhower was elected president on the Republican ticket in 1952, ending a 20-year Democratic lock on the White House, he appointed Dulles to be his secretary of state. Or, as Cooper puts it, Dulles "finally got to be SecState after running for it three times".
Cooper also points out to me that Woodrow Wilson, the subject of an upcoming biography by Cooper, "would be the proper person to enlarge upon" my points of comparison between the U.S. and British systems. "He was the first real practitioner of comparative government and he did want to adopt features of the parliamentary system here."