It's only interesting because 8 million people live there, and many more pass through the city

This population size is greater than most countries, and the density and speed of commerce there is fairly unique, so it's a constant coordination problem and experiment on a large scale that people look to.

Think of NYC more as one of the Free Cities in the old world.

They aren't a top level government by any means but they're mostly left alone to have nearly unilateral control of their jurisdiction. New York City has some unique challenges with key infrastructure (like all of the trains) being controlled by New York State and the Federal Government.