Population density is not the be all end all. You need to have enough folks in place A who all want to go to place B at the same time.
This is why large cities and commuters railroads work. Enough people want t go into the city to work. So you get subways and such.
But how to you get enough folks wanting to travel from Somewhere Idaho to Middle of Nowhere Idaho to justify a train?
The Answer is, you don’t. Even in France you don’t get that. Basically French Railroads run on more of a spoke and Hub system the people realize. I wanted to go from Avignon to Tours, in order to do this I had to Basically take an Avignon to Paris train and a Paris to Tours train. Because those two links had enough traffic to Justify the trains. But Avignon straight to Tours did not.
Yes thier are local trains traveling all over but mostly they take you to one of these trunk lines. So you use a local to get to a trunk. A trunk (or a couple trunks) to get close to your destination (of if a big city then it takes you to your destination) Then another local to you destination. Or you get in your car and drive, And let’s not kid ourselves a LOT of people in France England and Germany drive. I was stuck in traffic in all three Counties in the last two years on multi lane expressways. So the locals DO drive.
This will be the situation in the US as well. But because of the size of the US you will need a lot more trains over every flavor. And our Cities in much of the US are farther apart. And in huge areas such as Montana or Alaska you simply are not going to be able to build a useful network.
So you have to somehow build a network or trains while dealing with the following issues.
Scale of the system. It would have to be much larger then anyone else’s (except China) and thus would cost more.
It will lose money in many if not most locations. And thus have to be supported by taxes of some flavor (not ver exceptable in the US)
Even in Europe people would rather drive. Reality is that folks take mass transit (trains, boats, planes subways or what have you) because various factors make private transport a pain. Be it cost, time, traffic density, cost of car ownership or government regulations)
Paying for it. As stated subsidizing mass transit is not popular and tribes in the 20th century were vied as for profit companies and should sunk or swim on thier own. So good luck changing that.
Paying for it part 2. Obviously you can’t build it all at once and equally obviously you won’t build it at ALL in some locations. So you are going to have trouble getting the bill to pay for this through Congress when you consider how many congressmen will be opposed to it for any of the follong reasons A). They are opposed on general principles, B) thier State or there congressional district will not get any/enough service, C) thier State or district will be one of the areas that will pay for (subsidies) other areas. D) thier voters are opposed to it for whatever reason and thier fore they the congressman is opposed as they want to be re-elected to office,
So somehow you need 50+ % of Congress and the Senat and all while a President agrees.
Basically thier are sound and valid reasons why Trains are not as popular in the US as Europe. And I think a lot of people over estimate how popular they are in Eurpe and missunderstand why they are as popular as they are in Europe. So I don’t think this is happening without HUGE (almost ASB) changes to the World, technology, the US population, US politics, US taxes or some such.
Mind you I am not against trains. I love trains. I ride them where and when I can. I read about them. I model them I belong to train related historical societies ect etc. But I am sorry they just don’t work well in the US. Heck they don’t work all that well in France.
And to get them in the US would be even more expensive because some things that are put up with in Europe would never be allowed in the US. For instance all the metro and underground and train stations that require stairs (not even escalators) Much less not having wheel chair access. And the way they approach access would not be acceptable in the US. In the US you would not get away with telling an 88 year old that they will only have 10 minutes determine the platform thier train was going to arrive on then to stamp thier ticket, walk from the station to the platform, walk up the stairs (of if you lucky find and take the small elevator that holds 3 people at the most) then get into the platform and look up on the ONE screen where thier car is, then walk down the platform to said car. Then climb onto the train (platforms are not at floor level) dragging your luggage (the conductor standing right thier is not going to help) then scramble around inside the car lifting your luggage and then finding your seat, All this in 10 minutes, in this case it happened 3 times on various TGV routes with 1st class tickets. All because they wouldn’t tell ANYONE what track the train was going to be on. In one case (we had been thier for over a half hour before the announcement and the train as it turns out had been thier longer. So they just chose not to tell anyone.
So if your great example of trains works like that then it will realy bomb in the US and will have to make a lot of expensive changes to get past ADA laws. Thus it will be MORE expensive then in Europe.
So good luck with that.