Where I live in the Netherlands the train quite literally stops in front of my door, as in my building that is ~50 meters from the train station where I can take a train every 10 minutes (15 on weekends) to any other city in the country, and even outside the country to Germany or France.
I'm even planning a Eurotrip by train this summer with some mates, I'd say the distances here are comparable to get from NL to PL for example.
And besides, how is it that the US is "too wide" for trains to work, but apparently building an equivalent highway system is perfectly possible? China is also a massive country, yet they have incredible passenger train options to get cross country.
A self-driving car can stop 2 meters outside your house on an arbitrary schedule. That's going to be the competition with trains in the very near future.
Not sure what you mean by the last bit - the US already has that highway system, and the local roads serving the last mile, because that last mile infrastructure already has to exist to get from public transit to your house.
China doesn't have the exact same problem because so much of the country lives in dense wall-to-wall housing, which sucks no matter how you spin it if you like having any kind of space to yourself.