Not very many of this ilk have ever held the nation's top elective office. I think it's safe to call the second through sixth presidents members of this group: while none held doctorates, all were prolific writers and political theoreticians of the first order. After John Quincy Adams, however, there's a long drought. One might make a case for Abraham Lincoln-some studies have placed his IQ on the order of 140 or higher, i.e., borderline genius territory-but apart from Lincoln, none qualify until Theodore Roosevelt.
TR did not have a doctorate, but his writings stand the tests of scholarship (I believe his naval history of the War of 1812, although dense reading, is still considered a/the definitive work on the subject). Then, of course, there's Woodrow Wilson: the consummate scholar in politics. But after Wilson, again, the drought.
No, you can't count Kennedy. Profiles in Courage was ghost-written by Theodore Sorensen. I'm not sure about Nixon's Six Crises, but my sense is that it was more I-was-there history rather than scholarship. Otherwise, since Wilson, forget it. Any presidential works have been intended for popular consumption and/or were ghost-written.
So...how to get more of what Harding (oh, the irony!) called "the best brains" into the Oval Office?