You don't even need to live in the future to have a very high density. Paris proper has a density of 50000/sqmi yet has simply and literally banned high rise buildings. There are 2 districts with a number of these (although low by manhattan standards, culminating at 100m) but they are relics of the 70s and none has been built since then.
What is probably the greatest advantage of very dense cities is that you can have a really great public transportation network. While the farther suburbs cruelly lack transportation, Paris proper is tightly covered, with the great majority of residents having less than 500m to walk to get to the subway (and some lines have stops every 200m).
In these conditions a post-car society truly is possible and we're slowly but steadily getting there, with streets being closed to cars one by one, and parking spots being removed by the hundreds month after month.
It should be noted that Manhattan is a lot denser than it is on paper. It's daytime population is more than double its residential population. Midtown Manhattan on a weekday probably has several hundred thousand people per square mile, rather than the 70,000 per square mile nominal density of the island.
Bingo. There are a ton of people who live in the other boroughs, New Jersey, etc. that commute into Manhattan for work every work day and even on the weekends for fun.
What is probably the greatest advantage of very dense cities is that you can have a really great public transportation network. While the farther suburbs cruelly lack transportation, Paris proper is tightly covered, with the great majority of residents having less than 500m to walk to get to the subway (and some lines have stops every 200m).
In these conditions a post-car society truly is possible and we're slowly but steadily getting there, with streets being closed to cars one by one, and parking spots being removed by the hundreds month after month.