I think your point is generally valid for the US. However, Chicago-NYC might be a bad example, since it actuality might be viable. The Shinkansen goes ~200mp/h and thus would be able to go back and forth in 4-5hrs. Given that trains are less weather dependent, can drop you off on there middle of the city rather than the outskirts and don't come with the same security theater you probably come out with a comparable time frame and more reliability on that connection. Things like connecting the west coast to anything but itself are completely unviable though because of the reasons you gave.
Newer trains can go 300+ mph, especially the levitating variety where noise is less of a factor. Given how long it takes to navigate through the unbelievable bullshit in most airports a train has a 2h head start the moment it leaves the station.
NYC to Chicago goes through a (smaller) continental divide though (the Appalachians) [ADDED in what's also a pretty built-up area of the country]. So HSR is problematic on that route. It's about a 20 hour trip today so cutting that by 2/3rds would be a significant achievement but probably still wouldn't be enough to make it interesting.
The somewhat controversial LA to San Francisco route through the Central Valley may make sense. We'll see in 15 or 20 years or whatever. Unfortunately LA is pretty spread out so you don't get the same downtown to downtown advantages that trains in the Northeast have.
The route that probably would have the biggest potential benefit is speeding up the Northeast Corridor to the point where Boston to DC was more practical vs. flying. Amtrak is apparently doing some upgrades but decided that the most aggressive improvements weren't cost-justified.
The Allegheny Front, where the continental divide runs between Altoona, PA and Frostburg, MD, wouldn't be a particular challenge for HSR, because they're good at hillclimbing, and the mass of the trainset is nothing like loaded coal trains or intermodal double-stack trains which currently frequent this area.
LGV Sud-Est has 3.5% grades, for example; the Pennsylvania Railroad (now Norfolk Southern) Gallitzin-Horseshoe Curve-Altoona stretch is 1.85%, B&O (CSX) Sand Patch Grade further south is 2%.
Rather, overcoming the general ruggedness of the terrain is the greatest expense. Slower railroads can meander along rivers, but a HSR needs large sweeping curves (with large radii), requiring expensive fills or cuts or viaducts. Some tunnels would be needed to cross some of the linear ridges, just like the Pennsylvania Turnpike (and the predecessor railroad that used the same right-of-way) did. In fact, it's likely that an alignment would closely parallel the turnpike, as the landscape gets significantly more rugged south of Maryland or north of I-80.
A gentler route following the Empire Corridor (roughly, NYC->Albany->Buffalo) may be cheaper to construct, but would be considered a "detour" by a casual observer -- and the expense of the NYC->Albany portion may not make it worthwhile.
Sadly, it's not very likely that such a Mid-Atlantic-to-Chicago passenger-only railway could be economical to construct and operate. US infrastructure costs routinely run much higher than the international average for comparable projects, and even the as-the-crow-flies distance (1100+ km, 700+ miles) between NYC-Chicago puts it too far out of HSR's ideal range, even in countries where people actually ride trains.
If they built that route what's the likelyhood it wouldn't also have stops in Philly, pitsburg, Cleveland which would add significant time. I can't see it being a direct route with no stops inbetween.
All trains will stop at the first safe opportunity in the event of heavy rain, winds, or snow. It's one of the reasons (no level crossings is another) there has never been a fatal accident involving HSR in Japan.
