There are a few reasons trains didn't keep going in America, for transporting people.
Trains at their start, mostly focused on moving goods, most companies that offered transit only really did it to shill how nice their railroads were to business owners. Some routes, like the transcontinental line served an important purpose of moving people across the country easily and quickly.
Cities tend to be rather spread out and past the east coast, the population density drops on average This makes building a line out to these locations not worth it to the companies. Even if it had lines for freight, most of the companies running them might have a had a car for passengers but when the highways came in, they completely stopped since nobody wanted to ride the train.
All modern rail companies in the US don't run freight. Amtrak is the only passenger rail "company." Its partly funded by the government and is operated as a "for profit" company. The company operates most routes at a loss, there are not enough people riding them. They make most of their money running people between New York City and D.C. and other major metro areas. However, routes between smaller cities and towns don't have enough volume to make money but they run them anyways because its apart of the deal to get government funding. Amtrak also doesn't own most of the rail their routes are on. The various freight companies do and they will sideline any Amtrak train since they give priority to their own trains.
A catch-22 has fucked American passenger trains, Trains are seen as slow, so people don't use them. Amtrak doesn't get money because nobody is riding the trains so they have to make cuts. Making cut result in further slowdowns.
Short of the government seizing the rails and operating themselves, trains won't catch on. Planes are objectively the fastest way to travel and cars let you explore the average American city much better since you don't have to rent a car once you arrive.
