Why future presidents appear in Harding's administration

Why did Harding's administration include several future presidents?

Senior public office provided an established route toward a presidential candidacy, making some future candidates recognisable before they ran.

Calvin Coolidge and Herbert Hoover are among the officials identified in the cabinet discussion who later became president. The explanation offered is that senior office gave prospective candidates experience and a public record before they sought the presidency. Observers could follow those careers as politicians moved between offices. The comparison with modern media concerns how national recognition can arise more quickly through publicity.