I think a lot of it is historical. America and Canada had virtually unlimited land for growth, so everything just sprawled outward. In Europe you're crossing multiple countries to travel the continent like you said. Since space was always a concern, more thought has been put into the designs and layouts. There are enormous American cities with poor public transit, and even if they had good public transit, it would take a long time to go from one part of the city to another. We've seen thoughtful layouts and good public transportation in dense cities where it makes sense, like SF, NYC, and Seattle. Cars are convenient for urban and rural sprawl, and there wasn't a lot of motivation for alternatives until recently.
BTW, you can cross the United States in a train too, but it'll take you 79 hours.