I’m not sure that it’s the sprawl either. Many European cities with large suburban areas around them and nearby smaller towns that have effectively become part of them (e.g. Milano) have frequent local/regional rail service out to all the suburbs and associated towns.

I wonder if US sprawl is still structurally different from European sprawl. In Europe even suburban areas seem more likely to have a small mixed-user core on which residents can easily walk to a train stop. The US seems to frequently deter that with zoning dividing residential and commercial areas

You either arrange your town so everyone can walk to the rail station, or you end up with Los Angeles. My favorite example is the Swiss city Chur. This negligibly-populated, irrelevant little town, which is 4% the size of San Francisco, has a 12-track rail station that is much better than the one that San Francisco plans to have by 2050. And, of course, the trains come constantly. In the next hour Bahnhof Chur will enjoy the arrival of 13 trains, and that's their pre-dawn service!