The Skyscraper Museum has [1] an exhibit on the history of density in NYC: https://skyscraper.org/housing-density/history/. Density was maximized in the slum tenement era at ~1000 people/acre, achieved with merely 5 story buildings (and somehow packing 10 people per apartment which just... how). The closest you've come since that era in NYC is London Terraces, which is essentially a block of residental rowhome high-rises. If you look immediately around it, you can see that most high-rises instead opt for the towers-in-the-park model.
Density tends to come not so much from height but lot coverage, and for various reasons, people insist on really low lot coverage from tall and supertall buildings, which puts extra constraints on density you don't get in mid-rise buildings.
[1] Or rather had, as they apparently swapped the exhibit out a few years ago, though much of the material remains online.
Density tends to come not so much from height but lot coverage, and for various reasons, people insist on really low lot coverage from tall and supertall buildings, which puts extra constraints on density you don't get in mid-rise buildings.
[1] Or rather had, as they apparently swapped the exhibit out a few years ago, though much of the material remains online.