If poor people aren’t driving in then it means that they are not a source of the reduction in traffic. On the other hand, if only the wealthy drive in then are we saying the wealthy are price sensitive? That seems very unlikely! Someone is not driving in as much.
There's a very large lower-middle to upper-middle class that is going to be price sensitive.
And that's the point. Maybe I'm pretty well off but $15/day is still painful for me to drive in every day. But! Occasionally I REALLY need to drive my car in to the city, so instead of driving in five times/week I just drive in once/week. That's 80% fewer trips, a huge reduction.
The people who aren't driving as much is the large group of well-connected assholes who have been abusing the city's parking placard program for decades.
You'd sort of have to live in NYC and observe it first hand to know this, since for curious "reasons" (like the existence of NYP plates) the NYC media doesn't cover it this way either, but it's true.
The other group not driving as much is the people who are semi-indifferent to driving versus transit but the money tips them one way instead of the other. Which is tons of people.
I think your explanation makes the most sense. getting the slack out of the system and reducing corruption plus driving some marginally middleclass to opt for commuter rail because $50/week puts them under.
For many commuters, though, it would suck if you're used to driving in but now have to take the LIRR (and xfer at Jamaica or whatever) or now drive to the PATH station and take the commuter rail in.
Sure, but that's because you can "squeeze" the price on people. You can't squeeze the price on something where there is no negotiation or haggling.
If you can get your plumber to do the 400 job for 250, are you gonna say, nah, here man, take 500? Who would do that, only lonely people looking for some company. (pool boy/wealthy lady, waitress/guy with too much money)