i dunno about the density argument. you're not connecting everyone with everywhere. you're connecting generally large metros with other large metros. texas central railway wants to start by connecting houston to dallas. that's a metro with 6 million being connected to a metro with 6.5 million. distance is about 225 miles. so that's 12.5 million people connected at about 55,500 persons per mile of track.
lets compare the tgv system. paris is huge by itself at 12.5 million, but no city it connects to in france is anywhere near that big. the second largest area is lyon, at 2.2 millon. so that's 15 million people connected, at a distance of about 280 miles. that's 53,500 people per mile of track. so that's lower than houston to dallas.
marseille is about 1.9 million another 170 miles on down. lets throw in valence and avignon on that line for about 2.1 million. that's 48,000 per mile of track. again, lower than houston to dallas.
at some point you connect over to san antonio and austin which are about 2.4 and 2 million, respectively. houston to SA is about 180 miles, and SA to dallas is about 250 miles, so for about 700 miles of track you've connected metros currently home to about 17 million people, and maybe 20 million by the time they'd get done. lets call it 28,500 people per mile of track connected (and that's it if's a full triangle connection, which it likely won't be, houston to SA probably runs NW to the college station area on the currently planned track, then cuts over to the austin area).
anyway, texas central isn't asking for any state support and is aiming for all private funding*, but shockingly the mouthbreathers in this state are trying to slam the door on it because, well, f--- infrastructure.
*the japanese gov't is probably making loans to finance some of the construction by the japanese firms that are involved, but who gives a crap if the government of japan wants to spend money here?