You can do Sacramento–San Francisco–San Jose–Los Angeles–Las Vegas–Salty Lake City–Reno–Sacramento (round trip) in 2500km as the crow flies, with as longest stretch 700km (SLS–Reno) and an average of 300km (of course you can then branch off and make lower-speed connections to towns in between). Checking inhabitants on Wikipedia for a few real quick, it seems they're bigger in my imagination (or in movies perhaps) than in reality, e.g. Reno is only like 200k inhabitants, but at least to/from, say, Los Angeles, which is a small country in itself from my Beneluxian perspective, there has to be travel demand. Or between SF and SJ, they're so close and there's other stops you can make in between. Hard to retrofit into a city if there's no existing train or metro that can at least pave the way to the edge of town, but otherwise it's hard to imagine it wouldn't earn itself back in a handful of years if it doesn't exist yet.
Across a continent east-to-west is obviously less practical, same with any other continent, but it looks to me like connecting big cities that are similarly nearby as European big cities isn't the problem. It's probably more about everyone needing a car anyway, extremely low fuel prices, public transport is deemed for peasants, no good walking/cycling/bus options to/from stations, that sort of issues (it's a thing here as well, a rich German has a lot of trouble getting into a bus when they can drive something fancy instead—of course I'm generalizing and this doesn't apply to every German with money).
I didn't write my comment with "as opposed" sentiment in mind, but can't help to wonder what is the typical distance between US capitals. So, wow, thanks for that piece of data!
I also think there's a hen and egg problem. To build a rail road you need to buy the land strip between two stations, and in today's US you can't just do it because someone knowing about your venture and how you cannot succeed without having all the land - will just ask any enormous price knowing you won't have a choice. I think the whole idea of hyperloop was born on that restriction - because buying places for support pillars and making the whole system more or less silent making it at least viable.
In EU railroads are there for 100+ years, all the land under them is belong to government or railroad companies.
Just did some doodling in OsmAnd, connecting a few cities big enough that I've heard the name (at least I'm presuming that's why I know their name).
https://snipboard.io/0aunhF.jpg
You can do Sacramento–San Francisco–San Jose–Los Angeles–Las Vegas–Salty Lake City–Reno–Sacramento (round trip) in 2500km as the crow flies, with as longest stretch 700km (SLS–Reno) and an average of 300km (of course you can then branch off and make lower-speed connections to towns in between). Checking inhabitants on Wikipedia for a few real quick, it seems they're bigger in my imagination (or in movies perhaps) than in reality, e.g. Reno is only like 200k inhabitants, but at least to/from, say, Los Angeles, which is a small country in itself from my Beneluxian perspective, there has to be travel demand. Or between SF and SJ, they're so close and there's other stops you can make in between. Hard to retrofit into a city if there's no existing train or metro that can at least pave the way to the edge of town, but otherwise it's hard to imagine it wouldn't earn itself back in a handful of years if it doesn't exist yet.
Across a continent east-to-west is obviously less practical, same with any other continent, but it looks to me like connecting big cities that are similarly nearby as European big cities isn't the problem. It's probably more about everyone needing a car anyway, extremely low fuel prices, public transport is deemed for peasants, no good walking/cycling/bus options to/from stations, that sort of issues (it's a thing here as well, a rich German has a lot of trouble getting into a bus when they can drive something fancy instead—of course I'm generalizing and this doesn't apply to every German with money).