The average doesn't really matter, though (and yes, I get that's a different argument than the other person made).
The threshold where you exceed what is viable does. And hardly anyone in the US live in areas that have so low density that there aren't viable routes, on the basis of comparing with the density of routes that are served in other countries.
Even, say, Wyoming, with an average population density 1/5th of Norway, has half its population in its top 10 towns, most of which, unsurprisingly, has rail going between them because a sufficient number of them are close enough to each other to form viable clusters.
Or, as I mentioned elsewhere, we have Montana, with a similar population density and a size ~50% larger than the United Kingdom, but a population 1/70th, where the lines that used to be used by the North Coast Hiawatha goes through a range of towns and surrounding area that easily covers ~40% of the state population at a density easily comparable to e.g. continental Europe and well above areas of rural Europe that are well covered by train.
There are many pairs of cities in the US between which rail travel is not viable. But there are very few cities that are not within a viable distance of a set of other cities with higher density corridors (than their state averages) in between that combined makes travel viable between them. "Nobody" will travel the full North Coast Hiawatha route between Chicago and Seattle, as it'll take ~48 hours. Plenty of people will travel parts of it (and do travel parts of it, as many parts of that route are still covered by trains). Including through some of the lowest density parts of the route if it is reopened.
To again bring up Norway, because I know the rail network there having grown up there, consider the line from Hamar to Åndalsnes - a line where the two most significant towns on that stretch have populations of around 3k (Åndalsnes) and <30k (Hamar). Compare to e.g. Butte, MT (~34k) to Billings, MT (184k). Both again are within similar distances to several more cities that form similar viable pairs and that that similarly enhances the overall viability of the connecting segments. And that's part of why Hamar to Åndalsnes is viable too - it connects to a couple of other lines at Hamar and at Dombås.
Just like Butte is a viable distance from Spokane via Missoula, and Billings is a viable distance from Gilette, WY, or Buffalo, WY (still larger than Åndalsnes, and has rail) and onwards to Cheyenne, WY.
I'd actually love a map that visualizes which parts of the US are sufficient "islands" that there are towns of any reasonable size that are not within those kinds of travel distances along a reasonable rail corridor to make up a total population size along the route that is large enough to be considered viable plenty of other places.
I can't think of any.
The US as a whole is huge and dispersed and low-density, but almost nobody lives in the low-density places, almost by definition - even as large as they are, they're not large enough for the low-density population that lives in those places to add up to significant numbers. And the upside of a train over planes is that it's not the end-to-end distance that matters, but the population near enough to the stations along any given subset of the route.