Washington, D.C.'s location was always primarily a political solution. That said, Washington himself and many other backers of the District of Columbia believed the Potomac would become a major artery of trade with the trans-Appalachian west, not just uniting the north and south but the Atlantic coast with the west as well. Fear of losing the west was an important motivation in many early political decisions. Talk of Kentucky's secession (or even defection to Spain) struck terror into statesmen of the early republic.

The development of the Potomac as an artery into the West was a longstanding obsession for George Washington, who'd surveyed the river's western reaches. He was the main force behind the Potomac Company, which was chartered shortly after the Revolution's end with the intention of building a canal from the Atlantic to the Ohio. The canal ran into technical, financial, and political problems, and wasn't finished until decades later. However, the lessons of the failed experiment made the federal government much more interested in facilitating interstate cooperation for future infrastructure projects.

Check out Joel Achenbach's The Grand Idea: George Washington's Potomac and the Race to the West.

Capital accumulates where it's easiest to do business; therefore, the simplest answer can be boiled down to geography. Manhattan Island is arguably the greatest natural port in the United States, which allowed for a robust trading community to expand and a healthy system of credit to build. D.C.'s Potomac was a troublesome, inland swampy river to navigate, as was the Delaware near Philadelphia (New York City's greatest competitor during the Early Republic) which was prone to freezing over. Few could argue with the space and ease of travel with which New York harbor and Manhattan Island offered. The publication of the Commissioner' Plan of 1811 indicated that the growth of New York City was expected to continue and the opening of the Erie Canal in 1825 sealed the deal. The geographical ease of doing business from the Great Lakes to the Atlantic and Europe was centered not in D.C., but in New York City.

See: "City Life" by Witold Rybczynski and "Empire City" by Kenneth T. Jackson

Do any professionals in the sub think that D.C.'s building height maximum may have limited its population growth over the past few decades?