Why does it cost less to fly round trip from New York to Boston than it does to take Amtrak?
Basically, the airlines have been subsidized substantially in a number of ways -- particularly the airports, but my favorite is the wonders of "bankruptcy financing" where companies which go bankrupt just keep getting more cash pumped into them by very stupid "investors". Warren Buffet has warned repeatedly that the entire airline industry has run at a loss over its entire history, overall. Amtrak from New York to Boston is run for profit and makes a profit. Yes, really. (The profits don't cover the national overhead, as I mentioned before.) They can get people to pay sky-high prices, so they do so, and they profit. Why does the P100D cost more than a Toyota? Because it's what the market will bear.
Also, Amtrak trains are regularly 1-2 hours late and the quality of the service on the trains is pretty bad, compared to the rail systems in just about every country.
That's another story. It's true in much of the country -- though certainly not from New York to Boston. This relates to the insane system we have where the tracks are owned by private companies, which is true in pretty much *no country in the entire world* (Canada and Mexico are the only others I can think of where the tracks are mostly privately owned, and their passenger rail is just as bad and nonexistent, respectively). Everyone else nationalized the tracks. Where the tracks are owned by government, such as New York to Boston, Amtrak is typically not very late (I mean Italian rail levels of not-very-late, not Japanese punctuality).
(Actually, Mexico and Canada nationalized the tracks too, they were just idiots and later sold them off to private investors for less than they were worth. Canada actually did this *twice*. Actually, in the Northeast US, *the US nationalized the tracks too*, in Conrail, and then later sold that off to private investors for less than it was worth. There's a whole discussion possible on this bizarre philosophy of "privatize the profits, socialize the losses".)
The thing is, privately owned tracks are like privately owned roads, which approximately nobody advocates for. It just doesn't work well. England actually tried privately owned roads and gave up on them in the late 19th century. This does provide the only known test case for what you get if you have privately owned roads *and* privately owned railroads (spoiler, the railroads win). If the road system in this country were completely privately owned, Tesla wouldn't stand a chance. (That's not going to happen. I hope.)
Where the government owns the track, sometimes they do set up their own railroad (NJ Transit, etc.), and hey, sometimes they are operated better than Amtrak. But a lot of the time for smaller states like Maine or Maryland, the financial issue comes up that they don't want to cover all that *overhead* -- a maintenance base, a ticketing system, etc. It's better to defray that over lots and lots of trains. Amtrak can typically make an offer to operate the state's desired trains at marginal cost plus a small profit margin because their fixed overhead is already there and doesn't change; a competing offer would have to include a huge lump for overhead.
The economics of capital-intensive sectors of the economy which have network effects is actually fascinating. Most people don't understand it at all.
The way these economics work is also the reason almost all of the US has monopolies (occasionally duopolies) on broadband Internet, and it's more expensive Internet than in most of the world, and it's slower and less reliable; whereas places with municipal broadband have cheaper, faster, more reliable Internet *and* it tends to make a profit for the city. I'm not going to go into detail as to why this is, but if you understand this stuff, you're going to be well ahead of most investors in understanding capital-intensive sectors of the economy.