We should just ban private vehicles in the city as well, bringing back more cyclists, walkers, and generally increasing metro usage.
It has. It'd be illegal and extremely dangerous to design a city without properly functioning infrastructure for emergency services, garbage disposal, physically impaired accessibility. Also very inconvenient to not include commercial deliveries and public transit into that list of essential road use scenarios. Most of the vehicles performing these services are heavy.
For the most part only private ICE cars are light enough to be a drop in a bucket on the road maintenance. Private EVs, and especially EV SUVs, are likely making an impact on the maintenance schedule though.
You would essentially be cutting most of NY off from the rest of the world.