If anything, a higher-density city should be more amenable to bicycles. Standard passenger cars are tremendously wasteful of physical space. You can fit half a dozen bikes in the road space that a car in the city requires (meaning, including following distance). Then there's the amount of space they take up when they're idle, and the extra space for them to maneuver past each other safely.
The mass of automobile usage has completely warped our civic spacetime in this country. I'm not saying there's anything wrong with cars per se -- they have important uses -- but they certainly don't help with density of all things.
Amenable means open and responsive to suggestion; easily persuaded or controlled. NYC is none of those things. Yes cars take physical space but I think you underestimate the diverse needs and populations that drive the use of cars vs. bikes. Commuters from Westchester county are not going to ride bikes. Frail elderly people and de-conditioned office dwellers are not going to ride bikes.
Comparisons with Northern European cities simply do not make sense however much people would like to force fit them
The mass of automobile usage has completely warped our civic spacetime in this country. I'm not saying there's anything wrong with cars per se -- they have important uses -- but they certainly don't help with density of all things.