Lots of comments here about public transit or whatnot in the DC area. Virginia is about the same size as maybe Hungary or Czech Republic and about 60% bigger than Ireland. The area being discussed here is not in the DC area but about 50 miles/80km south of there between D.C. and the State capital Richmond. The nearest area to this disaster is Fredericksburg which is a small historic town and an exurb from D.C. around 50 miles/80 km away from D.C. and about 60 miles from Richmond.
It truly is in the middle of nowhere with most turnoffs going to farming/rural areas. In European terms it's similar to the stretch on the A4/A6 between Vienna and Bratislava, but about 2x as long and about half as populated. If you drive here you basically see nothing but highway and trees for a couple of hours, with the occasional turn-off into a stand of fast food restaurants and gas stations and really nothing else until you get nearer to Richmond or head a bit east towards Hampton Roads.
The local towns simply don't have the support infrastructure to clear the roads and wrecks and the state. This combined with a drop in temperature from over 60F to under 30F (15C to -0C) in a few hours and a massive snow drop caused the early falling snow to melt, then freeze into a solid layer of ice before road crews could salt the entire 110 mile stretch between DC and Richmond.
Predictably the result was a giant mess, and few areas for motorists to exit onto local roads to get around the affected area or get food, gas, or other provisions. There aren't even many hotels as options in the area given how rural much of this part of the state is. Google maps has simply marked the entire 110 mile stretch of the Interstate as black and provides directions around the entire thing on local farm roads.
Directions from New York City to Miami Fl (which typically use mostly I-95) simply route around that part of I-95 from Baltimore, Md to just North of Richmond using local roads, a distance of 152 miles (244 km) or about 3 hours driving, and includes crossing bridges over the Potomac River in incredibly more rural areas.
Another way to look at it is that D.C. is the southern-most tip of the heavily populated D.C. to Boston megalopolis mega-region and any further South is basically farms and wilderness until Richmond, the next distinct and different metro area from the North-East mega region. This problem has occurred in the gap between those two areas.