NYC to Philly - 95 miles
NYC to Washington DC - 225 miles
NYC to Boston - 220 miles
Washington to Bostin - 420 miles
NYC to Philly - 95 miles
NYC to Washington DC - 225 miles
NYC to Boston - 220 miles
Washington to Bostin - 420 miles
Not in my experience. I took Amtrak from Atlanta to DC in 2008, and it was basically a 13 hour flight -- same kinds of seats, only marginally more space, and the food service amounted to paying exorbitant prices for awful sandwiches that could have been vended from an office machine. I would prefer to spend 10 hours in an airport and 3 hours in flight, given the chance; airports are at least quite comfortable, in general.
The times I've taken Amtrak (mainly for amusement value; Seattle-SFO and SFO-DEN), it was mainly old people (many of diminished mobility), some religious groups (mormons? menonites?), and foreign tourists. And mostly empty seats.
Amtrak is expensive because it's expensive. It bills its sleeper service as a luxury thing, and charges luxury prices. There's nothing to say that it has to, or that anybody who decides to compete with them has to.
http://en.wikipedia.org/wiki/Couchette_car
proper sleeping cars where you have your own private small room are a lot more expensive.
I'm guessing it's a land availability problem: the existing tracks aren't straight enough, and building new tracks through these densely populated areas would destroy tens of thousands of homes. What we really need to do is travel back in time to 1920 and set aside some nice dead-straight sections of land for future rail works. Or perhaps we need to wait another hundred years and hope that building a 300-mile tunnel becomes affordable.