Your point is good, but it turns out that a lot of really expensive parts of Manhattan aren't anywhere near as dense as they should be, such as:
https://www.google.com/maps/@40.744212,-74.0017042,3a,90y,34...
https://www.google.com/maps/@40.744212,-74.0017042,3a,90y,34...
I'm not sure what you're getting at here.
I live in the area (in fact, I grew up there too) covered by the link you posted and don't know what you mean about density.
Yes, many of the older buildings are only 12-15 stories tall, although a bunch are 20, 30 or even 40 stories tall.
And yes, there are many brownstones (usually 4 or 5 stories tall, with 1-2 apartments per floor) on side streets as well. And there are buildings like mine (5 stories tall with 4 apartments per floor with a lot size of ~4,000 sq ft.).
But there are zero single family homes.
Or are you suggesting that we bulldoze Central Park and build 500-600 60 story residential buildings because Central Park is wasted space?
As a Manhattanite, not having Central Park (or Riverside Park, or any of the other greenspace in Manhattan for that matter) would make upper Manhattan completely unlivable.
Please do elucidate on this. What mechanism could significantly increase the density of Manhattan housing?
This ought to be interesting.