Places with really good train infrastructure tend to be places with really high population density. Even in China, there isn't great train infrastructure everywhere, just in areas with very high population density. The areas with low population density such as the mountainous regions don't tend to have lots of great train service. It's particularly good in the highest population density regions.

Similarly, Japan has great train service since there are 250 million people on a small series of islands.

Europe is another example, where a relatively large number of people live in large dense cities throughout Europe. Many Europeans come to North America and assume travel will be similar to Europe where you can visit a bunch of places in a short period of time because they're relatively close together, and then are shocked for example to learn that it takes 4 days to drive from Toronto to Winnipeg and most of the area between is just bush with little to no people living there. Winnipeg only has about a million people. Saskatoon and Regina are only 250,000 people each. Calgary is about 1.4 million and Edmonton is about 1 million, and even in BC you're only getting 3 million people province-wide in a nation 30% larger than the entire nation of France. When you take a flight over the country you see huge forests for hours at a time. The US is different of course, but lots of parts of it aren't that different. There's some highly populated areas, but there's some similarly unpopulated ones and whereas a plane simply ignores those areas, a train needs to travel through every inch.

There are regions with train service in America. In Canada, I've been on good trains in Vancouver, Toronto, and I've also taken trains in Ottawa. In all 3 cases it was the highest population density in Canada. There are also decent trains in New York and California, both regions with high population density.

Under both capitalist liberal democracy or authoritarianism, the construction of a common good requires two things: enough people to justify doing the project, and enough other stuff going on (or potentially going on in the future) to justify the project. Under both systems you burn through different forms of capital to get these projects done, and so eventually the laws of physics will pull you to the ground if you're doing wasteful things that don't help the people or the state.

In both cases, a certain solution must compete with other solutions for time and money. In the case of trains, they compete with planes for long distances and cars in shorter distances. The benefit of trains is they can carry overwhelmingly large numbers of people very efficiently and so if you have the population density you can carry lots of passengers and so justify your rail system. On the other hand, if there just aren't that many people then there just isn't anyone to use the system and so you're using all these resources for basically nobody, particularly if the potential users have other options and so take a car or a bus or a plane.

In the early industrial period, the monopoly trains had on travel allowed a lot of inefficiency. Railway companies built entire towns were built every so often to ensure there was water and coal for trains, and there were also stores in each so people could buy stuff along the way (or for those living in the towns) and in those towns the railway was virtually the entire economy but there was no other option for travel so that level of inefficiency for passenger travel was nonetheless justified. I went to one such town. All that's there today is a clearing, a railroad track, some building foundations if you look carefully, and an unkept graveyard.

Having higher population density would justify lots of investment in trains because you'd have so many people to move. The regions of China and Japan with great train service are highly populated, and to justify really good trains everywhere in Canada and the US, you'd need high population density everywhere. Towns of 5000 or 10,000 people would need 10x that number of people, and regions with nobody in them (of which there's lots) would need lots of people.

Given that the geographical reality is that North America has much more favorable geography than the bulk of China which is largely unpopulated and doesn't have many trains as a result, to have the equivalent would easily require 8 billion people to justify a really great investment in continent-wide rail. Even that may be a low estimate given just how much space we're talking about and the scale required to justify all the expense. Planes only require an airport at the source and destination and a plane. Considering that there might be only a few dozen major destinations, it is obvious why air travel has essentially taken over the long range travel market.

When it comes to climate comparisons, I think it isn't so simple as "trains use less fuel per passenger". To get from new York to California by rail you'd need to destroy huge amounts of nature, and burn through massive amounts of energy, including in the production of steel and concrete in unimaginable amounts, particularly for high speed rail systems. I suspect the calculus might not be so favorable in that light, especially if the trains are mostly empty because they don't solve a problem in many cases along American routes.