Far Rockaway is hardly densely populated.
The high Queens numbers are because of all the people who don’t need to live in a “cool” place but need to get to work on the subway.
I still have to disagree with you. There are a lot of very dense housing in Manhattan, Bronx, Brooklyn and Queens; as such, there would be a lot of close contact between people even before getting on public transportation. It’s a wonder how Hong Kong with its even denser housing per square mile managed to avoid a major medical disaster.