Nowhere near the density
Suppose that I am lazy and only want a 2 minute walk? Well obviously I lose some options. Like the choice of supermarkets, several out of all of the things I had several of, but for all but bars I still have several left.. And it becomes worthwhile to mention a liquor store, drycleaners, and choice of grocers.
The density of options is tied to the population density. There are all of these stores, restaurants, etc because there are enough people for them within an easy walk. There are enough people because the people have taken to modelling for sardines.
Given my druthers, I wouldn't be in NYC. But if I am going to be here, I might as well get the maximum convenience...
Cheers,
Ben
"... I couldn't see how anyone could be educated by this self-propagating system in which people pass exams, teach others to pass exams, but nobody knows anything."
--Richard Feynman