Not having to wait on a street corner for a crosswalk signal or only doing so sparingly would save NYCs on average more time than the occasional taxi ride. On top of that, the absence of cabs would set many minds on the problem of moving all New Yorkers around the city as fast as possible. If you're rich and you think that your time is valuable, then vote for spending on public transportation innovations that benefit everyone equally.
If you eliminate cars and time truck deliveries well, you can engineer a transportation system that runs like a well engineered clock with many complications. Cars are responsible for most of the non-detrminism in a public transportation system.