That price is far from typical for this service. The prices I quoted are what I just pulled off amtrak.com for a Friday NY-DC train on 12JAN18. A couple months ago I purchased a ticket from Fredericksburg (south of DC) to NY with only a few days in advance for only $130. Thee ten-trip option my sibling poster mentioned gives you the same flexibility you mention there. Please do not base your idea of the cost of rail travel in the NE US based on one very overpriced trip.
Edit:
Just saw your screenshot. That $295 is for the Acela (which is premium service). I just ran the same search, and midday trains are running about $152 for the NER and $168 for the Acela. The one you chose is literally the most expensive non-first class ticket you could book tomorrow.
I still don't see his $300 ticket, the only thing I can think of is that he's looking at a return ticket, but then that doubles the price on the Accela.
I've checked again for tomorrow morning, $295. Perhaps I'm using the site wrong: https://imgur.com/TnuOGt3
295/226 is $1.30 per mile.
I'm ignoring the slower trains, non flexibile, booking in advance etc, as that wasn't what was raised. There are slower options for London-Glasgow that are nowhere near the full price (for example £57 tomorrow morning if you go via Edinburgh - saving £130).
I've just checked my emails - last time I took this train (albeit from NY to Washington), in March 2013, it was $498 for 2 tickets - $249 each.
This is for a far less flexible ticket than I get in the UK. For my $240 I can travel London to Birmingham, have the day there, and then continue to Manchester, have a meal and stay in a hotel overnight, then get a train from Manchester to Glasgow the next morning.
Washington to New York is half the distance, and nearly twice the price, as London to Glasgow.