There needs to be local public transportation infrastructure. This is where the US should be focusing efforts, no long-distance high-speed trains. It works in Europe because there are huge catchment areas (see population density) that funnel riders to regional hubs that are then connected with high speed trains. I don't think the first step to making rail work in the US is connecting metropolises with high-speed trains. Until there's a better local public transportation story, it's expensive and impractical once you arrive at your destination.
But that not the point. Many of these borders are arbitrary e.g. it's like saying that Paris has a lower population Berlin even though such a claim would make no sense at all.
- Great Lakes
- North East
- Texas Triangle
- Florida Super City
- Bay Area
- Southern Cali
And of those the Lakes and the North East are perfect to connection. In all of them trains are massively underused.
Frankly some of these couldn't be more perfectly placed for trains.
But I do agree with your point. You need good local public transport. Or in more general terms, land use. Infill development, bikes and reliable bus system that is not designed to serve only poor people that don't have other options.
Really, what it seems the discussion should focus on is those shorter (but still quite long!) journeys that people would likely want to do. Train lines in California seem to make a lot of sense. A quick look on Google Maps suggests there's no train between San Francisco and Los Angeles which seems insane to me!
1. Walking (including wheel chair and friends)
2. Biking (including some slow electric stuff)
3. Rail based transport (trains, metros, trams as appropriate)
4. Buses
5. Private vehicles
I agree that Europe is more densly populated than US, so there would be longer stretches without a stop in the US. But that's OK - the long-distance trains in the EU don't stop at every station along the way anyway, it would just be a different structure of "locals" and "through trains" to service the poulations.
I disagree however that population density is even all that relevant. All the cities in the US that I've mentioned have rail through them already. It's used profitably for freight all the time. I think the US doesn't have good passenger rail service because of a heck of a lot of other factors - subsidies favoring cars and planes over rail for transit, infrastructure having been created around getting everyone an automobile, a huge amount of FUD from various lobbies against rail (including arguments about population density), and a dozen others probably have more actual impact than "people per square mile is different on average".