Not being an American I have no reason to even be a UA customer let alone install the app, and therefore I don’t know if they’ve achieved this or not.
Overall, choosing Amtrak or flying is perfectly reasonable in different situations. Amtrak could definitely be improved a lot though!
[1] For reference, I live near Miami (technically, I live in Boca Raton, but Miami is "close enough" at this scale). The company I work for is based in Seattle. I refuse to fly anymore for a variety of reasons.
[2] Riding in a private rail car really spoiled travel for me: http://boston.conman.org/2015/08/05.4 But way out of my pay grade.
(But maintaining the track to this quality would be even more expensive if there was as much freight on it as tracks in the USA carry.)
Edit: why the downvotes? You can get flights for 50 bucks to go to different countries in Europe.
The cheapest flight I can see on SouthWest.com is $60, for a 1 hour journey from Atlanta to South Carolina.
The cheapest flight with Ryanair from Copenhagen is $9, though it doesn't include checked luggage. It's also an hour.
An even cheaper one is Kraków to Eindhoven, 2 hours, $6. There are fewer dates for this price though.
They look very much in the style of Ryanair with the garish website. $22 for three hours (Boston-Miami) is priced between the two Ryanair flights, so I expect the "service" is similar.
I'm sure the average distance of a flight within Europe is lower than in the USA, since the USA is a bit empty in the middle and Europe has more water in the way, but routes like Scandinavia to the Mediterranean (Stockholm to Zagreb is 3½ hours and $14), or Britain to eastern Europe (London - Cluj, 3 hours $13) aren't far off, and the budget airlines also have flights to tourist destinations in Egypt, Israel, Jordan etc, which are as long as a US coast-to-coast flight.
While I enjoyed camping and seeing bits of the US that foreigners like me don’t normally see, it’s not entirely clear that the difference between that and flying makes flying the luxury.