Low population areas generate less traffic and less pollution. Let them be, for now.
Focus on the 80%.
Also, in-settlement transport is the US problem. It's probably fine if a lot of inter-settlement transport remains by car, except for connections between cities of say, more than 200k that are closer than 300km from each other.
As I found while replying to another comment, most of the largest towns even in Montana are already connected by rail, they just haven't had Amtrak service since the 70s after cuts. Just reinstating that would be a significant improvement, and most of the counties covered by the rail network in Southern Montana have banded together to try to bring passenger rail back again on that route.
And by that measure, we're mostly there. Chicago, New York, Philadelphia - we're good.
The next step would be to get reliable public transportation to the small towns in the Sierras of California.
My choice of Montana was for the size and the population density.
The issue sit hat the distance from {small town} in Montana to nearby city is much greater than in Norway.
If we're only going to do the eastern seaboard, ok. If rural areas are going to be ignored... ok... but there is a lot of rural area in the United States.
The idea of a train station (paved area next to the track) next to every small town in Montana with regular service to the nearby city (like Japan and Norway have) is impractical in Montana.
It is sometimes challenging to understand the sparseness of the Great Plains of the United States without having traveled through there.
Public transport outside of the large cities... the 10th largest city in Montana is Anaconda with a population of 9,000. There are 60 cities in Norway with more population than that. The 100th largest city in Norway has a population of 5000... if it was in Montana, it would be the 20th largest city.
Yes, let's start solving this in the largest cities and that will get most of the population... better public transportation and better electrical infrastructure. However, the approach of "just need more train stations" (yes, a simplified straw man) isn't going to work in most of the US when looking at it by area.