Wasn't the parkway built specifically as a main highway between DC and Baltimore? IIRC, it was the first limited-access highway between the two cities. It should've been expected it would draw a lot of traffic and become a major highway.
Though they were not Interstate highways, several of the NPS Parkways in and near Washington, D.C. were built to provide a highway under federal control and ownership between D.C. and military bases located outside the city. So far, some of the parkways have been used
one time to get troops to and from D.C. - during and immediately after the April, 1968 riots in D.C. following the assassination of Rev. Dr. Martin Luther King, Jr.
The B-W Parkway was built in part to provide such a connection between Fort George G. Meade in Anne Arundel County and Washington - and in particular to provide a high-speed road to the National Security Agency (which moved to Fort Meade in the 1950's not long before the parkway was completed).
The southern George Washington Memorial Parkway was built to the south to provide a connection to George Washington's Mount Vernon, but also to provide a federal road connection to Fort Belvoir (though between Mount Vernon and the gate at Fort Belvoir, VA-235 must be used).
The northern part of the GWMP and the Clara Barton Parkway were built to provide a highway connection to what is now called the Naval Surface Warfare Center, Carderock Division on the Clara Baron Parkway near the Maryland end of the American Legion Bridge. In the past, U.S. Army troops have been encamped there for some reason in tents, even though this place is a U.S. Navy base.
The Suitland Parkway was built to provide a connection to Joint Base Andrews (formerly Andrews Air Force Base), even though the D.C. part is now maintained by DDOT, it is used by dignitaries (foreign and domestic) to travel by highway between Andrews and downtown D.C.