The very reasons why the Big 5 work are the reasons it could never quite take hold in DC:
1. No central arena. Even before Verizon Center, there wasn't a place big enough to serve as a court everyone could get along with--Uline was a dump, the Armory never took hold, AU and GW were marooned at Ft. Myer until the 1970's, McDonough was too small, and Cole Field House was neither neutral nor centrally located.
2. The Big 5 has had five schools at a similer competive level. But in DC, you've had three steady programs (Georgetown, GW, Maryland), but some have come only recently (American, George Mason), others dropped out of Div. I (Catholic), and Howard has never taken hold of the city in basketball.
3. Philadelphia's Big 5 works, at its core, because these are city schools and, with the exception of Penn, still attracts lots of Philly kids to these campuses. Georgetown, GW, and AU attract only a small percentage of students from the local area, with Mason and Maryland at bookends across the region. Internationally oriented schools have a tougher time focusing on city rivalries.
4. The Big 5 began and was nurtured in an era of basketball independents. Now, with six or seven DC schools in six or seven different conferences, loyalties lie elsewhere.
5. Finally, it was tried before, sort of. In the late 1950's and early 1960's, there was an attempt to brand Georgetown, GW, and Maryland as "the Big 3" and play a home and away series among each for an unofficial title. Maryland backed off from two games a year in the mid-60's and Georgetown-GW went to a single game each season in the 1969-70 season. Bottom line, it never captured the city's attention.