The contours of a successful HSR system in the US and Canada are roughly as follows:
The core linear corridors of DC-Boston (densest US population) and Detroit-Quebec City (that's 10/15 largest cities in Canada). Combine these with an east-west Boston-Toronto and north-south Montreal-NYC spine (timed interchange at Albany makes too much sense), as well as several other small feeder routes I'm not mentioning.
A Midwestern knot centered on Chicago with lines to (in ccw order) Minneapolis, St. Louis (maybe to Kansas City), Louisville (and thence to Nashville I think), Cleveland, and Detroit (not sure how to squeeze in Cincinnati and Columbus). At this point, you might consider connecting the tendrils to the northeast system as well.
CAHSR, with connections to Las Vegas and Phoenix. Texas Triangle. Maybe Portland-Vancouver.
Nashville-Miami via Atlanta, and Atlanta-DC via Research Triangle in NC.
Further I don't think you understand the cost, lot's of people out east think throwing a rail line together isn't more difficult than throw a couple of logs on the ground and some metal tracks. Let me tell you about what it is like trying to build a rail line through the west. There are mountains that make the Appalachins look mighty tiny that you've got to dynamite straight through, because you can't go up them, with the alternative being massive detours. If you want to go through the south you'll have hundreds of miles of tractless desert with temperatures being over 100 degrees on the regular, without water for miles.
Connecting the 19th and the 46th largest city over ~400mi of mountainous terrain with no intermediate cities of note to pick up along the way is not a recipe for success.
> Further I don't think you understand the cost, lot's of people out east think throwing a rail line together isn't more difficult than throw a couple of logs on the ground and some metal tracks. Let me tell you about what it is like trying to build a rail line through the west.
That's why I didn't suggest any routes like that. The closest you get is Portland-Vancouver, which is questionable in large part because of the mountainous region (and Portland, OR is quite frankly not a large city). CAHSR does have to cross two or three mountain regions (depending on how you count), but you're connecting 40 million people in several large metropolitan areas with it, so it's actually worth it. And outside of those, I'm not connecting anything else--you're the one complaining that I'm leaving out Denver-SLC after all--so how do you think I'm ignoring the expensive costs of what I'm not proposing to connect?
Low population densities can be misleading; much of the US is highly urbanized, and dense urban centers would be very efficiently connected by rail service were we to improve it. I for one would almost certainly make more trips to cities in Ohio, Illinois, etc. if it was a < 6 hour high speed trip rather than an overnight one.
[1]: https://en.wikipedia.org/wiki/Alphabet_Route