I'm thinking that if we look at the numbers we might actually find it makes the problem worse, but in other areas. We have very heavy traffic areas currently, but spread over at least a few square miles, which allows that traffic to route to the available spaces through all the available roads. Giant parking structures at specific points along rail would move a large chunk of that traffic to those structures, but those structures are also much more condensed points for traffic
Simply put, if you think urban traffic is bad, imagine trying to get to a specific parking structure along with a couple thousand other people all at the same time. Instead of a thousand different businesses over a hundred or more roads, it's a few structures, each with limited ingress and egress routes, and limited entrances and exits. Worse than navigating the parking structure at the mall at Christmas, but every weekday as the new normal.
Much better, in my opinion, would be a fleet of autonomous buses and vans with ad-hoc ride-sharing. Since they use the normal road system, they can reach much closer to peoples homes. I actually ran the numbers on this in a comment a few months back (although not very thoroughly)[1].
I suppose it would be nice to build tall, dense housing around the station, but people living in the suburbs are expressing their preference for more, cheaper space per person and lower building heights, and would be extremely unlikely to authorize a microcosm of the city inside their suburb.
If we can solve the "people don't want tall buildings" problem, why not put them inside the city where their occupants are in walking/biking distance, rather than relying on expensive trains?