Efficient planning could overcome that. A central hub with lines going to every other major hub nearby would be enough to connect all the cities. Then each route can run "express" services that only stop at major stations along the way, and "local" services, which stop at every small station. That way people can travel faster between hubs, while stilling giving access to less populated areas.

A few transcontinental lines for high-speed trains, and some major north-south routes as well, make public transit a viable optipn for long-distance travel.

Each city having its own metro system would make intracity public transit a viable option, reducing the need for cars and therefore reducing traffic congestion, simultaneously making it possible to make neighborhoods more walkable. A few spoke-shaped lines to reach out to surrounding suburbs, and loop-shaped lines to connect the outskirts without having to tranfer at the central hub.

Then all you need is a few well-planned bus routes to connect suburban areas to nearby stations. The only ones this leaves out are rural areas, who would still depend on cars, but that's a much smaller portion of the population. Eliminating the need for a car in urban and suburban areas would go a long way towards reducing congestion and pollution.

Lots of places already have good public transportation systems, because they were built around the premise of using trains as a main mode of transport. Suburbs are built around train stations. Mixed-use zoning allows for as many residences as possible to be constructed within walking distance of a train station. And since there's less need for parking lots, they can be built more densely to avoid wasting space.

The car lobby in the USA did a lot of damage, and now it would be costly to convert the infrastructure. But long term, it would be a worthwhile investment.