I don't know about other cities, but to understand the strong political push back against congestion pricing in NYC requires a bunch of local context.
Neither the rich+, nor the poor, nor the vast majority of the middle class regularly commute into Manhattan by car. The poor and the lower/middle middle class because parking is prohibitively expensive. The upper middle class and the rich because they either live in Manhattan or they'd rather take commuter rail than sit in traffic. To the extent the latter take ubers or similar such services already pay congestion charges and there isn't too much fuss (except from the drives who don't have much political muscle).
The bulk of car commuters into Manhattan are instead those with de jure or de facto free parking. That's largely government workers (e.g. teachers, cops, firefighters) and members of the trades (i.e. construction workers).
For those with de jure free parking congestion pricing isn't a big deal, whatever authority is setting aside parking will either pay the congestion charge or get it waived. It's the beneficiaries of police and traffic control refusal to enforce the law with respect to certain favored populations that are up in arms about congestion charges. Because a congestion charge is likely to be enforced by an automated mechanism which, unlike parking control, will not engage in public corruption on their behalf. And these groups, unlike the uber drivers, do have a great deal of political muscle.
+At least the ordinary rich, hecto-millionaires and billionaires might be a different story