Just for a little perspective, I lived in Japan for 15 years, a country with a little less than half the U.S. population in a land area the size of Montana. About 70% of that land area is too heavily in forest and mountains to permit much human habitation. And, yet, is is one of the most pleasant places on earth.
People are not the problem. Even population density is not the problem. The problem is the type of people and the policies.
The people who reside in Manhattan Island also import virtually all of their food. They generally eat once a day ~ and in the long run of history that sort of behavior can lead to some interesting societal conventions if they should start running short of food.
Check Flores Island! Nothing but little tiny people with giant heads all over the place.