But what if charging what the market will bear means the rich are paying for the cost of the thing and then some?
Anyway, my impression is that opposition to things like congestion fees come more from affluent commuting suburbanites than the poor (who probably already rely on transit anyway).
No, because the point is that cars specifically are Pretty Bad for cities (noise, air quality, inefficient use of space, dangerous) and should be discouraged (and economic incentives work). Mass transit is generally far less bad and should be encouraged by economic means.
NYC sort-of does this by not using zone fares, so long trips from far-away areas (read: poor parts of the city) cost as much as a brief trip through a rich area.
Because of geometry: cars do not scale well in cities. Only so much land to go around, you want (need, really) people to use more space-efficient modes. Supporting cars is particularly expensive compared to other modes because of how much space cars take to move around and park.
Anyway, my impression is that opposition to things like congestion fees come more from affluent commuting suburbanites than the poor (who probably already rely on transit anyway).