Right, but it's exactly the same in London. The only people who are regularly driving into central London are either professional drivers (taxis, delivery vans, etc), for whom the charge is just an operating expense, or they're very wealthy. Just parking in central London is going to cost you a lot more than the £15/day congestion charge.
In addition to the central congestion charging zone, London also has an additional £12.50 low-emission zone (ULEZ) charge targeted at older, higher-polluting vehicles. The ULEZ has now expanded to cover all of Greater London.
You forget that America is a car culture outside of NYC so a typical tourist coming to NYC for the day will likely just eat the cost and drive anyway. The geography of NYC is also very challenging. A lot of the public transportation options don't even cover places like Staten Island properly so people drive instead. There won't be much of a difference in traffic imo. Taking the train is already pretty expensive.
In addition to the central congestion charging zone, London also has an additional £12.50 low-emission zone (ULEZ) charge targeted at older, higher-polluting vehicles. The ULEZ has now expanded to cover all of Greater London.