As a federal district, Washington, D.C. operates quite differently than the typical American city--or territory or state, for that matter. It was only in 1973 when D.C. appointed its first mayor and city council. There is no congressional representation for its residents. The district is mired in budget problems since it is up to Congress to draft and pass its budget.
So, should D.C. have a bit more autonomy? As discussed in the video below, the policy was intended to insulate and protect lawmakers. In addition, efforts to give D.C. full statehood have never built up momentum in Congress--lobbying efforts for the cause are prohibited and rural states are opposed. States like Wyoming and Oklahoma do not want new members of Congress who would likely represent interests that are in line with urban, densely populated areas like D.C.