Why is Amtrak so darn expensive in the Northeast US? I just looked up a train from New London, CT to Boston, MA (a 2 hour car trip); the round trip cost for two people was $200. Traveling by rail in Europe is significantly cheaper; any ideas why?
As noted elsewhere, you cannot take the price of a single itinerary on a single route on a single date and make conclusions about rail travel on a single service compared to rail travel on an entire continent.
Even if you could, it would not hold. I tried some bookings for 27 February at 0800. Amtrak's Acela Express would be $78. SNCF quotes me 70 EUR (~96 USD) for Paris to Brussels, DB quotes me 59 EUR (~81 USD) for Hamburg to Berlin, and a Hikari train on the Tokaido Shinkansen from Shizuoka to Shinagawa is 6,180 JPY (~61 USD). But on a short trip like this, there is no reason to take the Acela, as the Northeast Regional is almost as fast, and would only cost $36.
But Amtrak costs what it does fundamentally because the price of transportation depends on supply and demand. While the balance can be distorted by things like subsidies, the constraints on both explain why a flight from DC to New York costs as much as a flight from DC to Los Angeles, even though it is only one-tenth the distance. And in this respect, Amtrak remains broadly competitive with other modes of transportation along the NEC.
Ten years ago I never took Amtrak; why would I when I could get from Downtown DC to Midtown Manhattan, door to door, within 3 hours, for $116 round trip on the Shuttle? Nowadays, with more rigorous airport security, capacity reductions, higher fuel prices, and transit service cuts among things, I would allot at least 4½ hours and $340. To drive would also take 4-5 hours, and entail almost $60 in tolls and $50 in gasoline, plus the stress of driving I-95 and the New Jersey Turnpike and then finding parking. So Amtrak offering me a round trip for $260 is compelling. (yes, there is the bus as well, but it's as uncomfortable as the plane and as slow as Amtrak and as dangerous as driving, so naturally you should expect a discount.)
And while Amtrak does not practice price discrimination as ruthlessly as the airlines do, this may partly explain why your NLC-BOS ticket seems overpriced: they don't want someone riding NLC-BOS if they can sell the same seat for more profit to a NYP-BOS passenger.
Travelling by train in Europe is not necessarily cheaper, so your premise is false.
Some examples on flexible tickets:
If you want cheaper train tickets, travel more slowly, book earlier, or travel at off-peak hours.
(Warning: Much of this answer is opinion, but I think that will be true of any answer to this question.)
(EDITED to remove the point I was mistaken about.)
For many years, the US base assumption has been private car, followed by airline if you can afford it or intercity bus if you can't, with intercity rail a distant third. The passenger rail system receives little to no government support compared to the highway system. (Which is one of several reasons we mostly don't have true high-speed rail yet.) The history of how we got here is complicated, but that's where it stands.
Commuter rail lines are better supported, heavily used, and much more reasonably priced. That may again be a matter of population density, and of commuter traffic jams making non-roadway solutions more attractive.
At least the Northeast Corridor has fairly regular rail service, and has "higher-speed" trains through the BosWash section. Other areas and longer runs are often operating on a single train per day.