Can you imagine how much traffic there would be if NYC didn't have the MTA? The principle of induced demand tells us that as long as there are roads they will have roughly constant traffic because people are willing to spend some roughly constant amount of time getting to and from destinations by road each day. More roads speeds up everyone's commute which brings in more drivers, which brings traffic right back to the baseline terribleness.
The question is how shitty it would be if they also had everyone on them who's currently on public transit.
So basically, it is a traffic-free panacea for everyone who chooses to use it. It's not a goal of trains to eliminate traffic for everyone who insists on driving.
https://www.tomtom.com/newsroom/explainers-and-insights/indu...