Funny that no one has mentioned the Alaska Railroad. While it doesn't have daily service on its routes, it does seem to offer more than a "cruise train" experience...
Sorry, but no. The Alaska Railroad has been a cruise train for upwards of 30 years now. (In part because that is what makes money, not providing basic transportation, and they are in business to make money.)
I rode it between Fairbanks and Denali a number of times while I lived in Alaska. The train did not even stop in Nenana, Anderson, or Healy, though in the 90s Nenana and Healy were still listed in the timetable. Something upwards of 95% of the passengers get off at Denali Park. A tiny handful of through Fairbanks-Anchorage tickets.
When I was going to college in Fairbanks, I enquired about riding to Anchorage at the end of the term - got laughed at. In the offseason it ran once a week (north Saturday south Sunday) so I'd have had to stay in Anchorage for a week, and it cost considerably more than a plane ticket.
They do still offer the bush service between Talkeetna and Hurricane Gulch (where the railroad travels one river drainage farther east than the highway,) sort of the way VIA offers the minimal amount of service they are required to in the Canadian far north. But they quit providing that type of service to the rest of the state, where they are "only" a few miles from the highway (and sometimes on the opposite bank of a river with no bridges), a very long time ago.
That said, both ARR and Princess (or whomever has since bought them out) DID offer exceptionally good service at not-completely-outrageous prices for the Denali rides, and I can easily imagine that kind of service and pricing working on any number of scenic Amtrak routes. There could be 5 Princess cars going from Denver to Grand Junction every day, but there aren't...