Yes there are very empty places in the US, turns out though that the vast majority of people don't live in those places. The dense places in the US are dense and massive like anywhere else in the world, and if suburban sprawl makes them somewhat more spread out that is just pointing out how bad the status quo is with city planning/mass transit.

Also.. ok so the distance between two cities is vast... a highspeed train is far more efficient at transporting people (at absurdly higher volumes) over a distance than aircraft are. If it is a popular route between cities I dont see how distance negates this inherent advantage. Yes, if we we talking hugeeee distances that means a massive infrastructure investment but there would still be a major advantage in the end?