No, it's a scam that will backfire and ultimately end in regression. You can't just get rid of cars. You have to replace them with something. Working people will feel the pain of this because the trains are already way too overcrowded.
Punitive measures in the absence of constructive measures will absolutely fail. This isn't complicated.
This would be a more reasonable argument if we were talking about a city like Dallas. Manhattan is one the most transit oriented cities in the US. Bus, ferry, and train service already exist. All that require would be an increase in frequency as people leave their cars.