The founders of the USA, specifically the Federalists of Washington's and Adams' administration had ambitions for DC as becoming the new Rome, the center of the federally centralized USA, and to make it into the largest city in the western hemisphere. However when Jefferson came into power with the Jeffersonian revolution he not only halted all centralization efforts by the federal government, but also completely halted all development on the capital itself, calling it unnecessary federal expenditure and causing the government to be working out of literally half finished buildings for the next several years.
If the USA had stayed on the federalist course (heavily centralized east coast state with the interior of the continent politically subordinated) could DC have fulfilled their ambitions? With the federalists in power the Louisiana purchase becomes much more unlikely, and without the midwest territory and the canals into the great lakes built by the state governments New York City would be much less likely to take off as much as it did in development. Similarly without New Orleans which was the largest city in the US at the time of its acquisition the Mississippi river delta remains under the control of foreign powers, and even if the USA conquers its way inland in colonial wars it still is hampered by the bottleneck at the delta.
Really I am just fascinated in imagining how the society planned out by the early founders, especially Hamilton, might have taken shape.