Even Montana, which is a favourite example of mine when the discussion of US density comes up, because it has no passenger service connecting the towns in the S

Even Montana, which is a favourite example of mine when the discussion of US density comes up, because it has no passenger service connecting the towns in the South, and is very low density, has a density along the old Southern rail corridor that operated until the 70's that is similar to existing viable passenger train lines in Norway. There certainly are stretches in the US that aren't worth covering by train, but as you say most people don't live there, and the proportion who do live there is really tiny. A lot of the time people seem to think the end to end travel need to be viable, and ignore that if the service is regular enough, plenty of pairs of towns along the route will contribute to demand.