We have lots of commuter trains near large cities in the US. Many people who work in NYC, Chicago, Washington DC, and the like take commuter trains into and out of these cities from surrounding towns and cities. The issue is outside these big metro centers, most of the US isn't as densely populated to make this feasible.
I think by international standards the idea that American cities usually have trains is not right. Basically there are five urban agglomerations with useful train service in America and the other cities have one train a day (that may depart at 2am) or, usually, no trains. Can you get from Dallas to Tulsa by train? Absolutely not. But a city the population of Tulsa would have several trains per hour if it was in Switzerland or France or Japan.
The real situation is closer to "none" than "lots".