As for benefits/needs of a high speed passenger network--all I have to say is that my current options for going Chicago - New York which I do frequently are: 1. garbage airlines that are consolidating more and more and increasing their prices for no apparent reason, 2. broken roads that are constantly being repaired, and 3. Amtrak
That said, it's clear to me that a high speed rail connection (for example Chicago - NY at ~200mph) would be a no brainer. I'd even pay more than I pay American Airlines for the route.
So, instead of worrying about continent-sized high-speed rail networks, maybe we should start by thinking about building a high-speed rail network that spans the Eastern Seaboard states, where so much of the population is packed, then then expand out from there (Chicago, Memphis, New Orleans, Houston, etc.). We've already tried this with Amtrak and their Acela Express, but it's kinda lame: expensive and not that fast.
If we just built a seriously fast high-speed train between Boston and DC (stopping at NYC, Philly, and Baltimore along the way), and priced it competitively with air travel, then we'd be getting somewhere. Extend it down to RTP, Atlanta, and Florida next, and then a western spur to Cleveland and Chicago.
A separate high-speed rail network along the west coast, linking San Diego, LA, SanFran, Portland, Seattle, and Vancouver would also make a lot of sense.
What probably wouldn't make so much sense is trying to link the east and west coasts with such a system. Rail (even HSR) is just too slow to compete with air travel for distances that far.
Of course, Musk's Hyperloop idea might make more sense than any of this, though it'd basically be serving the same purpose in mostly the same way, just with tubes instead of rails. But its speeds would be even higher than air travel, so it could really replace air travel for major corridors, leaving air travel for places where Hyperloop isn't built yet, or for any travel which crosses large bodies of water.
For long distances, yes. For short to medium distances, high-speed rail can be much better. In the DC-Boston corridor, rail is already very competitive with air and that's with "high-speed" rail speeds averaging 80mph. True high-speed rail would be much better than air in that corridor.
I think you mean 'passenger railroads'. The US freight railroad is world-class. Lots of spurious debate about railroads in the US comes from confusing the pros and cons of a freight network (which we have) with the pros and cons of a high-speed passenger network (which we don't have). The benefits of a continent-sized high-speed rail network in a continent with low population density tends to be over-emphasized.
http://business.time.com/2012/07/09/us-freight-railroads/