I suppose there may be some rural routes where it's a good option, but I don't see it.
And that's to say nothing of extended networks - Amtrak is great if you live near an Amtrak station. A lot of people do not, and buses serve them well. Ish. For many places in the country, Amtrak is comparable to a slow plane, not a fast bus.
People under various hardships have different needs. Greyhound you can pay cash, if you don't have a credit/debit card, though you do need a photo ID. Amtrak is the same, but doesn't go everywhere. Megabus you can ride without a photo ID, but you need a credit/debit card and access to the internet.
When I was traveling that way there were a lot of families moving out of Chicago by bus, with all their possessions in black garbage bags.
Also, prisoners in Illinois tend to get a bus ticket when they're released: http://www.chicagotribune.com/news/ct-prison-releases-bus-me...
Amtrak from Dallas to Austin is a 6h22 trip for $29 (value fare), departing only once per day (11:50am) and taking about 2 hours to reach Fort Worth, a 30-minute drive.
By contrast, there are 11 Greyhound buses from Dallas to Austin per day, from $13-19, and the ride is never longer than 3h40 (mostly 3h to 3h10). There are usually 3-4 Megabuses in each direction per day as well, for around $12 for an unreserved seat.
Amtrak in Texas (and most of the rest of the country outside the NW corridor) is set up as a cross-country sightseeing/nostalgia tour service. Sunset Limited (New Orleans to LA) runs three times a week. It's not meant for actual, you know, transportation. Really, they ought to fully embrace that and operate more like a cruise ship with day stops for sightseeing. An American version of a Rhine cruise.
Probably this is because they can't compete on either price or time with busses, planes, or cars. I think there's many city pairs in the country where center-to-center rail service at a price and speed between bus and air would work well, but I doubt that can be achieved on the freight rail network.
I assume you meant NE corridor although I understand that Seattle to Portland by train works reasonably well. Even on the NE corridor it's really segments. Boston-NYC and NYC-Washington DC work well. Boston to DC really takes too long although I've done it.
There are some other segments here and there but even when they seem like a good way to get from A to B (like Raleigh to Charlotte), in my experience it's not heavily utilized.
They're still relevant because there is literally no alternative.
Interestingly I looked into bus travel to Oxford, Mississippi (home of the University of Mississippi) a while back. I live in New Orleans without a car, and I figured it could be an interesting weekend trip and assumed it would be something like $30 round trip by bus.
There is no bus or rail service to Oxford. Greyhound and Megabus no longer stop there. The nearest airport is in Memphis, Tennessee. Taking a cab from the airport or from the nearest train or bus station is impractically expensive.
The only way to get there is by private car. I'll go there someday if I buy a car, or if a friend of mine with a car feels like going.
To your point -- for really long distances, air travel is likely the way to go, but for regional transportation it is a reasonable alternative. A tank of gas in my Ford F-150 is as much as $90, making a bus ticket or a flight cost effective within the region.
Amtrack's schedules are fiction.
Some rural routes? Google for maps of Greyhound and Amtrak routes to see how many places the train doesn't serve.
I would seriously consider doing it for the experience / as a vacation (I like trains), but not as a serious mode of transportation.
Am I missing something, or are you able to sleep in the coach seats?
The actual beds aren't bad though, and the dining car food is decent.
At half the cost, I get it. It's not pleasant, but there are plenty of people for whom the money is a lot more important than the time. Particularly if you're not currently employed, for example.