To own a car in Singapore, a buyer must bid for a certificate that now costs $106,000, equivalent to four Toyota Camry Hybrids in the U.S., as a post-pandemic recovery has driven up the cost of the city-state's vehicle quota system to all-time highs.
NYC is a smaller geographic city (municipal boundaries - 5 boros) and has 2 million more residents. Try implementing this there for a tenth of the price and see if there’s riots at worst, and every elected official losing their next election at best.
Your math is off somewhere. Wikipedia claims that NYC has 302 square miles of land, while Singapore has 283.
This article estimates that the cost of owning a car in NYC is $3000-$5000 per month. So, you pay for the privilege, perhaps not as much up front.
But NYC is surrounded by places you can drive to. Singapore is not. The mainland city of Johor Bahru is a relatively poor city of only 500K people, and beyond that it’s farmland until you get to the Malaysian captial, more than 4 hours away. So I wouldn’t expect the two cities to have the same preferences for car ownership in any case.