It's not so much that our rail system is outdated as it is that it's purely optimized for freight. However, there are a lot of rail bridges that definitely need replacing that have yet to be replaced since rail companies are expected to replace them themselves in areas where it's exclusively freight rail that runs along those routes. Freight rail and commuters place very different demands on a rail system. Freight rail travels slower because it can still beat out trucks and planes for overland ferrying in terms of volume moved versus money spent, and because freight is so much heavier than transporting commuters, the trains can only go so fast safely before risking derailment or risking wearing down the railways faster than is cost effective. The only way true HSR happens on a consistent basis is if we build grade-separated passenger rail HSR infrastructure for all HSR routes.
And, yes, it certainly can replace some short-distance flights in the US (some of which are subsidized some by our government, iirc; though in some areas that subsidy is needed due to distance from anywhere significant), as it can offer equivalent or better travel times for shorter flights at its top speeds without the hassle of dealing with the various things that require you to arrive 2 hours before your flight's stated departure at an airport as well as with none of the pre-flight tarmac waiting to take off.
Taking Minneapolis to Chicago, for example, even a train with a top speed of 110 MPH along an existing freight rail route that was proposed 5 or 6 years back would be just 5 hours 30 minutes of trip time with stops in several towns and cities along the way. That compares to time spent at the airport and in the air that combines to be 3 hours, 30 minutes, assuming a 2 hour early arrival, which I generally recommend when flying out of either MSP's main terminal or ORD, and the airport travel doesn't factor in the travel time between ORD and Downtown Chicago, if that's where your hotel is, or the travel time from Downtown Minneapolis to MSP. The train's travel time also is an hour faster than the drive time between the 2 cities. And this is all with a train with a projected top speed around 110 MPH. Imagine what improvements could be done at nearly double that top speed.
(source a:
http://www.mnhighspeedrail.com/html/high-speed-faq.php, source b for car travel time is Google Maps, source c for air travel is a combination of Googling flights with estimated flight times combined with my own travel experiences flying out of MSP's main terminal).
Oh and from a productivity perspective, instead of needing expensive setups to provide WiFi on planes, trains can do WiFi using overland cellular service (at least in theory, though chances are trains are equipped with outdated and expensive equipment instead) or by having travelers just use data from their own plans.
I wish I could recall all of my sources from a paper I wrote specifically on a Minneapolis-to-Chicago HSR route back in college 5-ish years ago when Scott Walker decided to completely stop construction on the Wisconsin portion of that route even though the construction was already started on upgrades on the Milwaukee to Madison portion of the route (at least IIRC, can't find a source on whether construction had definitively started at this point). I had gone through a sizable cost-benefit analysis (at least as sizable as an 8 page paper written for a technical college can get).
