Those who originally built Washington (or kept to the original themes) believed in the political meaning of the institutions the buildings were meant to house. We didn't build a great mansion for the President. We built a great mansion for the people. Same with the Capitol. Those buildings were to reflect the great purpose and historical significance of their occupants and all they represented. For the architectural inspiration -- that same inspiration which guided the American founding itself-- we looked to the ancients.
Atop the Supreme Court building (constructed during the Great Depression!) are Roman figures. Why?
(Hint: it wasn't decorative.)
Re-read Machiavelli. He wrote history that looked forward. Amazing.