New York City already has a significantly higher population density than Tokyo (~11,300/km2 vs ~6,300/km). It's easier to develop more housing when you have more land.
Tokyo is 13400 sq km, NYC is 780 sq km. If I rounded Tokyo's land area to the same sig figs as I did for NYC, it would be lowered by half the total area that NYC takes up!
That's just not an accurate comparison.
Live in NYC. Lived in Japan. The difference is transit. It is far easier to get to Saitama or Kawasaki or Yokohama or Chiba than it is to get to Long Island from NYC. You can do the former in an hour at rush hour. Try getting to downtown Manhattan from Bay Shore as a daily commute. You'll go mad.
Here's Tokyo and New York at the same zoom level:
Tokyo: https://www.google.com/maps/@35.736739,139.6246444,10z
NYC: https://www.google.com/maps/@40.7983574,-73.948053,10z
The gray area of Tokyo on that map is pretty much all considered an exurb of Tokyo, more-or-less feasible for daily commute by rail. Most of the NYC region is inaccessible from Manhattan, except by car. Look at the Seibu Shinjuku line, or the Chuo line on the Tokyo map -- both offer express trains that will take you from the distant western exurbs, right into the middle of downtown Tokyo:
The density of the NYC MSA is 1/3 that of Tokyo: https://en.m.wikipedia.org/wiki/New_York_metropolitan_area
There's plenty of room to grow up. Just because the reason we don't is shitty government organization and FPTP voting doesn't mean we can just ignore the vast swaths of low-density just outside Manhattan 's borders.