New Delhi isn't even in the forty most densely-populated cities [1]. The city feels crowded because infrastructure has not developed with the population. If you want to see what happens when a government artificially cap housing supply, visit San Francisco.
[1] https://en.wikipedia.org/wiki/List_of_cities_by_population_d...
An interesting thing to notice from your link, Union City, Guttenburg, and West New York (all in New Jersey) make the list while New York City does not. This is only because of how the lines are drawn.
There is a lot of land around Delhi to develop the city laterally instead of allowing 4 floor construction on a 50 square meter plots on a narrow street. How to you allow for electricity, water, and commute without creating bottlenecks. Road are already conjested and new ones cannot be constructed easily. You can go underground and that's happening (Delhi Metro Project) but it's neither easy nor cheap to build an underground transportation system under a crowded city. It all comes down to appeasement and corruption going hand in hand.
SFO might be on the other side of the spectrum with its draconian zoning laws though.