Topography plays a factor as well. For most intents, DC sits on the piedmont line.
Not sure what being on the Piedmont has to do with - unless you want to factor-in opposition by certain groups representing wealthy people that live on the Virginia and Maryland parts of the Piedmont.
I was referring to the fall line that separates the Piedmont from the Atlantic coastal plain. As you well know, topography in the Piedmont gets a bit hilly with steeper cliffs near the river. This topography makes it more difficult to bridge the Potomac upriver from roughly Georgetown.
From Georgetown to just above Great Falls, yes, though the engineers that sited and designed the Chain Bridge, and later the American Legion Bridge seem to have managed O.K.
Above the intake for the Washington Aqueduct just upstream from the Great Falls of the Potomac River, and as far upstream as far you might want to go, it would not seem terribly difficult to build another bridge.
Only problem I am aware of was in the winter of 1995/1996, when a heavy January snowfall was followed by a nearly unprecedented thaw in most of the Potomac's watershed, leading to a massive rise in the waters of the river, which
almost swept-away the Point-of-Rocks (U.S. 15) Bridge.