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Your comments only apply to the US, and even then you're ignoring some highly used routes such as the NE corridor which is not occupied by wealthy retirees, but rather businesspeople, students, etc.   It also ignores commuter rails and urban subway systems that are well subscribed by working folks in many cities in this country, particularly on the coasts.  

Trains only function efficiently if you have sufficient coverage both in time and space.  In many countries including Japan and a good chunk of Europe, this has been achieved, and so trains are one of the major modes of passenger transport.  In the US, it hasn't, so it isn't.

Agreed in some respects...
Yes, there are actually areas of the US where it makes sense. That NE corridor is one of the VERY few. It's so because the population density up there is so much higher than most of the rest of the country. 
And commuter rail / light rail is IMHO overly loved and under-delivers on promises regularly. People romanticize it because they want to be the sort of people who ride light rail but would NEVER be the sort of people who lower themselves to riding on--gasp--the BUS! But often light rail becomes a financial boondoggle, ridership never actually hits the projections, and instead of acknowledging that, cities try to make up the financial burden by cutting bus service. Again they help wealthy suburbanites at the expense of the people who absolutely NEED reliable public transit. 
http://www.coyoteblog.com/coyote_blog/category/rail-and-mass-transit
Now, when the population density gets high enough, then commuter rail and urban subways make a lot of sense. But I don't think it's a matter of expanding coverage. I think that outside of the coasts, rail will NEVER be viable in the US. Why? Population density:
https://simple.wikipedia.org/wiki/List_of_countries_by_population_density
The US ranks 179th worldwide with 85 people per square mile. Much of Europe is 5x that or more. Japan is about 10x that. It completely changes the calculus.
I could go throughout Southern California from LA to San Diego by train / commuter rail. I could *maybe* justify a ride all the way up to San Francisco on the Pacific Surfliner if I didn't care about time and didn't want to drive. And maybe Phoenix/Tucson could work depending on what trains go there from here (I've never researched it). Anything longer than that is not viable. And this is in the US's most populous state. If I wanted to go to Portland or Seattle? Fly. Denver? Fly? 
And frankly given how close NorCal and Phoenix are, and given how ridiculously easy it is to find cheap flights, I'd probably just fly anyway. Especially given that the train seems equal or more expensive than flying. If I wanted to save the money, it'd be a bus. 
Now, if I lived in Denver, or if I lived in Salt Lake City, or if I lived in Lincoln, NE, or if I lived in Chicago, or Nashville, or Austin, almost EVERY place I might want to visit would be financially and schedule-wise not viable to go via rail. 
The bulk of the USA is simply too spread out to justify passenger rail. Really the only viable place for it is the one area that everyone points to trying to justify passenger rail for the whole country. But the whole US doesn't have the same population density as the Northeast. 

And commuter rail / light rail is IMHO overly loved and under-delivers on promises regularly. People romanticize it because they want to be the sort of people who ride light rail but would NEVER be the sort of people who lower themselves to riding on--gasp--the BUS! But often light rail becomes a financial boondoggle, ridership never actually hits the projections, and instead of acknowledging that, cities try to make up the financial burden by cutting bus service. Again they help wealthy suburbanites at the expense of the people who absolutely NEED reliable public transit.

Nice analysis overall (in the parts of your post I didn't quote I mean).  Agreed that many of the rural, sparsely populated areas will not likely benefit from passenger rail.

Only place I'd take some issue is with the generality of the paragraph above, which is based on an article of light rail in Seattle and Phoenix, primarily.  Seattle was a late adopter of light rail (much to the delight of Portland, ever in competition with their larger neighbor to the north) and it has quite a limited network (if one can even call a single line a network).  For example it doesn't extend to any of the neighborhoods north of downtown and only recently reached the UW campus as its final terminus on that end.  It's actually just a north south line from SeaTac to now UW.  So, no surprise that it's not well used as it's so limited in spatial reach.

Portland on the other hand, has continued to add lines, a new major one ever 5-10 years, including one that took me from my east Portland bungalo to my downtown university office at PSU, with only about 6 total blocks walking needed.  I could also jump on the light rail and be at the PDX airport in about 20 min, with no parking needed, at a cost of $2.50.  And, I never minded riding the bus either, as did a whole lot of other well dressed working folks that I witnessed.  Bus 12 went right down Sandy also stopping two blocks from my campus office so also very convenient.  

Anyway, certainly light rail/subways don't work everywhere as well as light rail does in Portland, or subways do in places like Wash DC or NYC, and so no doubt there are a good number of cases of Seattle and Phoenix out there, so your points remain valid for many.  Anyway, here's a wiki list on light rail (doesn't show subways), which shows quite a range of ridership:

https://en.wikipedia.org/wiki/List_of_North_American_light_rail_systems_by_ridership

I'm guessing there have been a few corks screwed and a few of the other zig zags on that trip as well

I seem to have inadvertently derailed this thread with my ill-advised Amtrak inquiry. 

medina, Very useful info; Hadn't occurred to me to look into getting to the Rutgers campus from Penn Station. I've used Penn Station about a dozen times for various trips in and out of Manhattan. Need to come up with a Rutgers trip now so I can see NYC again.

I used to take Amtrak from Chicago to Syracuse to visit the GF at Cornell. I could take it overnight, and as a college student, it was more affordable than a flight from Milwaukee to Syracuse (though I did that, too). Once, in February, the train broke down in Buffalo because it overheated...reportedly because it was working so hard to fight the brutally cold weather.

I ride the train, whether electric heavy rail (think DC Metro), or traditional diesel electric, every day for my commute, and I prefer the traditional one. It will go electric in the next few years (which is a great thing), and should get extended to downtown SF, which is even better. 

We're also thinking about taking an overnight train from here to Salt Lake and back for a family visit to Yellowstone, but that's probably at least a year out. This summer we hope to spend some time in Europe and expect a lot of train travel between major destinations.

Trains are a great means of transportation, but aren't well suited to sparsely populated areas, of which there are many in the U.S. For travel of under four hours, high speed rail would be a great upgrade over flying for a variety of reasons, but the U.S. public is skeptical for some reasonable (cost) and some bad (years of successful auto lobbying) reasons. We are decades behind the rest of "the west" on this, likely because in the 1950s we had so much land, so much industrial production, and so much oil. Our current economy is much better suited to trains, but we haven't recovered from our fixation on the car, and just because many areas of our country are suited for trains, doesn't mean all are.

The technology is easily there to get from LA to SF in under three hours, including multiple stops. It can drop people off at key locations, unlike the plane, when taking boarding and transportation to and from into account, it is faster, it is safer by just about every metric, including potential for terrorism, it is more comfortable, and it uses fewer resources. It is also more scalable. One of the issues with the LA to SF air route is that none of the Bay Area airports have capacity to expand any further; nor do the freeways into the Bay Area. However, California has--and will continue to--grow, thus expanding past the already over-capacity airports and freeways. 

This isn't to say high speed rail will replace all air travel; for some people--apparently including you--flying will still be a better option. But for people in the highest density areas of the state, high speed rail is a much better option--if only it gets built.

Its opponents are doing everything they can to drive up the cost because they know that is the most likely way to kill it. That includes recruiting as many people as possible to fight every proposal along the way. The public notice and comment and environmental requirements in the U.S. and California make a lot of sense in many ways, but also put up a lot of roadblocks that make it much easier to slow down or kill projects than in many other places. Democracy is not very efficient. The result of that is that political interest groups (including elected officials) look for every opportunity to force compromises that benefit them. Europe and Japan didn't have this big a problem with trains because cars didn't make as much financial sense there as they did here (because of higher density, lack of land, oil, and industrial production at the time the city-to-city transportation networks improved to more modern trains).

And recognizing the benefit of public infrastructure projects has always been difficult. The Hoover Dam finally made it through because it promised to generate electricity (it does, but that's hardly it's main purpose). The people of Boston hated the Big Dig (and hate it--meaning the process--still) because of the cost and intrusion, but they love the Boston it created. They have no trouble with the cognitive dissonance. People up here in the SF area complain that the BART extension to the airport cost too much money and doesn't impact them, but they would blanch at all those riders if they were put back on the freeways. Same for the CalTrain system. They worry that it doesn't pay for itself, but the gas taxes and car registration fees (even with the newly raised taxes) don't come close to paying for the roads we drive on (I believe the number is around 30%).

Public infrastructure is hard and expensive, and won't provide everyone a direct benefit, but it often provides secondary and tertiary benefits that people don't take into account.

And it's very possible that all the compromises that go into making the California high speed rail a reality will make what could have been a great boon to the state's economy instead an albatross.