You are making the same point I am without realizing.
For the rich, it's a negligible expense. For the poor, it's a major inconvenience (scenario you described) or cost.
So mainly the city expects it'll get free money out of the people who will still drive in. The only folks who will contribute to decreased congestion are the ones for whom $15/d is meaningful.
I think there’s much more of a sliding scale than that. Yes, there are very rich people who will drive no matter what. And there are a very small number of poor people who won’t drive no matter what. But in the middle sit a large number of people who are much more likely to use park and ride schemes and the like.
Good news is the city wins either way: if people still drive, city gets money. If people don’t drive, city has reduced congestion.
For the rich, it's a negligible expense. For the poor, it's a major inconvenience (scenario you described) or cost.
So mainly the city expects it'll get free money out of the people who will still drive in. The only folks who will contribute to decreased congestion are the ones for whom $15/d is meaningful.