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.
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'm only going on what you said.
MTA.info says this ride is 247.50 for a 10 trip ticket, with a trip of 85 miles that would be 247.50 for 850 miles, or 30c/mile.
From what I can see when doing a like-for-like comparison between the UK and the northeast US, the US is surprisingly pricier than the UK.
Now to be fare the Salisbury weekly season is valid for 10 journeys (or even 40), but only over 7 days, where as the Poughkeepsie one is a carnet, you can do 3 days one week, 2 days the next, and that's better, but for the Monday-to-Friday person, I'd rather be paying the Salisbury-London fare than the Poughkeepsie-NYC fare. (I'd rather be going into NYC, just without the fare)
Metro North also sells a weekly pass for $166.75. Unlimited rides during a calendar week. The 10-ride ticket has two prices, for peak and off-peak. Peak-hour 10-ride is $247.50, as you said; off-peak is $157.25.
Very few people actually buy a weekly pass on Metro North; either you are commuting infrequently (eg, weekend commutes) in which case you want a 10-ride ticket, or you are commuting daily, in which case you want a monthly ticket. A monthly pass between Poughkeepsie and GCT is $521. If you commute 20 days per calendar month, your per-mile cost is $0.16 / mile.
(Metro North fare information here: http://web.mta.info/mnr/html/planning/faresMar2017/hhfares_m...)
For the train route I myself am familiar with, the line between New York and Poughkeepsie, two different train systems serve the route, Amtrak (the company that does the nation-wide train service in the United States) and Metro North, a commuter-rail line associated with New York's MTA, via their Hudson Line.
I started with the Amtrak costs because the New York <-> DC train is an Amtrak train; most daily commuters will be using the Metro North, as it is cheaper.
The trip is approximately 226 miles. With sufficient advance purchase, the Northeast Regional coach fare is $49 each way and the Acela is $168 each way. I have never seen an NER fare greater than $200 each way. How did you arrive at $1.14 per mile at all, let alone thinking it's typical?