Thomas Jefferson believed that the rural farmer was the ideal of the American citizen. William Jennings Bryan preached something similar a century later. “Burn down your cities and leave our farms, and your cities will spring up again as if by magic,” he said in his 1896 “Cross of Gold” speech. “But destroy our farms and the grass will grow in the streets of every city in the country.”

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We can do without the cities, in other words.

At different points, they have been considered too full of immigrants, the poor, African-Americans, factories, patronage, congestion and disease. And their mayors have been almost structurally predisposed to antagonize rural voters. In the battle for state resources, whatever cities won, rural communities appeared to lose, a tension that remains today.

In seeking higher office, mayors from smaller towns could also be ridiculed for lacking experience.

“The challenge then when you go to the larger city is that it sort of opens a can of worms,” said Patricia A. Kirkland, a professor of politics and public affairs at Princeton. “Larger cities tend to be more liberal. And as a result, some of the promises that politicians might need to make and the positions they might need to take to build an electoral coalition might be difficult to justify later to more moderate voters.”

As a result, mayors have appeared less likely to seek higher offices of all kinds, including the more obvious steppingstones to the presidency. The other two mayor-presidents, Andrew Johnson of Greeneville, Tenn., and Grover Cleveland of Buffalo, were, like Coolidge, governors in the interim (and Coolidge ascended to the presidency in 1923 after Warren G. Harding’s death, not through election).

Mr. Palmer, the political scientist, and colleagues cataloged the career trajectories of nearly 700 American mayors in office since 1992 in the largest cities and every state capital (South Bend wasn’t large enough to make the study). Fewer than 20 percent of the mayors ran for higher office, fewer than 15 percent won a primary, and only about 5 percent won their races. Those are striking numbers for the mayors of the country’s most prominent cities, the researchers argue.

In related interviews with mayors for the study, the obstacles appeared to be not just how nonurban voters might view these mayors, but also how the mayors might view their job options.