> Car-owning households in NYC are significantly richer than zero-car households.
I have no doubt that's true, as in most other places on the planet.
The thing is, you are making an absolute argument: those who drive in NY are richer than those who don't. I don't deny that. I'm making a relative argument: within the driving group, the poorer ones will be priced out. You say those are not poor, but "merely wealthy". Our grand-father said they are blue collar workers. You both lack data, and I suspect that we will see a wide, gentle slope, with most rich people driving, but also an important minority of the lower classes, depending on personal circumstances.
The thing is, does the exact composition of the driving public mater for the regressivity to be a political problem? Some will be priced out and they will scream bloody murder, because from their perspective they were sacrificed in favor of the rich. You could go out and say "boo hoo, you are merely rich", but that's a politically imprudent move - a thousand personal stories will pop up about those marginal blue collar workers no longer able to feed their families.
So you could be right that it is not regressive in a broad, social justice sense, but that's not the sense in which the problem will be sliced. Rather, the vast majority of the affected merely rich will invoke the principle of the matter, and in principle it's designed to price out the poorer drivers, there's no doubt about that.
An idea I'm toying with is to distribute "tradable driving coupons" to all people holding a drivers license. A flat tax would develop on the market, so the net effect is similar to congestion charging. But now the tax does not go to the city, but to the poorer residents who opt not to drive. Ideally, fiscal credits should be earned, so as to not reward those who don't pay any tax and thus have no contribution to the infrastructure. This beautifully solves the political problem and makes driving a matter of personal choice: you are now rewarded for preserving the public good.