I've also seen rural US and Europe.
Trains work well when you have enough people to care to use the infrastructure. But if not, you might try buses. I saw a rural village in Hungary (~80 people) which has a bus stop to the nearest town. That's very nice, but the village center is a mile walk from the bus stop on the highway. My point is that a train may not automatically work. (Some rural communities in the USA do have similar bus routes.)
I'm curious: what is your example of a small European village with a train line? I'm asking because I just picked a random American town on the map: Spencer, Iowa. ~11k people, and it's about a two hour drive (~100 miles) in all directions to a larger city. A two hour drive is a decent drive, but it's not much overall, especially if you're comfortable driving. It's quite hard to find a similar scenario in Europe: these vast, sparsely-populated tracts of land. And that's my primary point: Europe's population is distributed more uniformly and densely than the USA. A blanket claim about how x transportation mode must be used in the USA ignores the stark regional variations.
Sure, in certain large cities, widespread car ownership may lead to a tragedy of the commons scenario, but it's on a per-city basis. The vast majority of cities in the USA will never encounter this problem because their "commons" are just so big, all cows still find a spot to graze. The cities that do encounter large traffic jams eventually build public transportation infrastructure to reduce the burden on roadways.
Playing out the maximal scenarios, I'd much rather live in a world where everyone drives cars than everyone rides trains. A mix of both is even better.
Walkable downtowns are great, and cities of all sizes should have them.