NYC has absolutely just as much of a NIMBY problem as other American cities it's just the government at large cares less and people don't worry about traffic in the same way suburban areas being upzoned do. 25% of manhattan has some type of historic designation around it. Additionally, during the same period where the brooklyn and queens waterfront boomed with construction due to targeted rezoning, huge swaths of manhattan were downzoned from hells kitchen to the majority of the east and west village.

Additionally, there are hundreds of thousands of people who are rent burdened in New York, even in those places with so called cheap rent such as within south bronx.

Just a note from someone who moved from NYC to a suburban area a few years ago: a car doesn't cost that much (as I thought anyway). Outside of the fixed costs, insurance is about $70 a month, and gas at $60 a month, so that's about $130 in total a month, just a bit over the $116 in unlimited train rides in NYC. (And yes the fixed costs are much higher, I will admit.)

You're forgetting the actual cost of the car itself, plus maintenance. The average monthly auto payment in the US is sitting aroudn $500. If you buy the car up front with cash, then you need to count the opportunity cost of that money over time, and depreciation.

And then there's also registration, emissions testing, annual inspection, and other miscellaneous fees that vary by jurisdiction, but that can easily cost hundreds per year in total.