One of the things transit advocates fail to grapple with is that our municipal political systems in the United States are broken. When it costs New York City 5-7 times as much money per mile of subway as it does Paris or London, you can’t build enough subway to meet peoples’ needs. (The debate over transit would be totally different if, for what MTA spends now, it was building five times as much track to meet peoples’ needs.)
Who would run the transit that goes from the edge parking lots to the city in your hypothetical? It would be WMATA. The same organization that, despite ample funding, let DC’s Metro decay to the point that they had to turn off automatic train control—a feature that was designed into the system at inception in the 1970s.
That’s the political reality we have to design our transportation systems against. Looking over the pond at what they do in Amsterdam or Paris is foolish—it’s like designing a plane for earth’s gravity based on what it would take to fly a plane on Mars.
During peak traffic in both of these cities I've been easily able to walk as fast as traffic, forget how much faster public transit or biking would be.
If you displaced all the cars within a city, then transportation within the city would likely be faster and more efficient for everyone. City buses would be much nicer if there was virtually no traffic in the city. Biking would likewise be a more realistic option if was dramatically safer and had better infrastructure for storage.
of course that's a pipe-dream, but the obsessive car culture in the US is a nightmare so it's nice to have some contrast.