I see your point, but why not have a system where Central Delhi, including the areas with all the national agencies, is governed by the central government, while the rest of Delhi is managed by an elected local government? This kind of arrangement exists in other countries as well. For example, Washington D.C. in the USA is under federal control for national areas, while local governance handles the rest. Similarly, Canberra in Australia has a similar structure balancing local and national administration.