I don't own, or plan to own, a car, but I still oppose congestion charges based on the marketization of basic public goods.
It's unfortunately mutated from the Economics definition to a more loose "good for the public" in public discourse, confusing everyone.
Street space in Manhattan is not a public good, because with enough cars using it, it becomes more and more useless. To fix that you have to make fewer people want to drive there some way. There are other methods than pricing, but they have problems of their own.
Very widely used methods are e.g. reducing lanes, reducing speed limits, banning (private) cars on some roads and decreasing parking space. These are used a lot more widely, and probably a lot more succesfully, than pricing systems. Notably these all are about as discouraging regadless of how much money you have.
In general the primary purpose of these pricings is to discourage people from using the priced thing, revenue from the fees is a bonus. The price naturally is more painful to pay the less you have money, so the less you have the more you are discouraged.
this kinda just exposes the depth of car-centric bias. to any competent urban designer, in a place like Manhattan, public transit is the "basic public service" and cars & roadways are a LUXURY.