Part of the problem with a city like New York is that it was a product of the two dominant forms of transportation of the respective ages in which is was expanding the most. First, the horse drawn carraige, and then later the automobile.
Neither is necessarilly the most sensible way to move about a city, but rather they were adopted out of convenience and out of a lack of better options at the time. If technology had allowed for subways and metros from the very earlier days of the world's largest cities, they'd be laid out and built radically differently.
We can see proof of all this in cities like Venice, where the primary form of transportation after walking is small watercraft, including their famous gondolas, and where there have never been automobiles and little to no horse drawn carraiges. Why did they settle on gondolas and bridges? Because it was convenient - the city was built on a river estuary in the Medieval period, and subsisted chiefly on fishing and trading via watercraft. And this choice of transit technology ended up shaping the city in almost every aspect.
New York city could, with proper planning and revamping of infrastructure, function perfectly well with absolutely zero automobiles. It'd be difficult to make the transition, but it is eminently possible and to many perhaps incredibly desireable. The reduction in noise, in pollution, in accidents and inherent dangers, in crowding, et cetera, would all be substantial boons to many urbanites. The trick is getting people onboard with taking the necessary steps to enact this sort of change.