That comparison is a little disingenuous, of course flying between two cities with an airport, that are not major hubs connected directly by hi-speed rail, will be faster and cheaper. Now consider how you'd get to Dusseldorf or Paris from whatever random smaller city with a train station (in western Europe basically any city with a population over ~100K). I'm not sure if there even are international airports around western Europe that arent directly accessible by train...
Besides traveling for business or pleasure, trains here are heavily used for commuter traffic as well. If you live and work close to a train station, which is quite common in the more densely populated countries, traveling by train will 100% be faster that sitting in a traffic jam every day. And in many cases your employer will even cover most or all of the cost (at least here in the Netherlands).
Obviously trains are still only point-to-point transportation, so if you need to be somewhere without a train station, or without many connections to larger hubs, you will lose time. But compared to the pitiful state of passenger rail in the US (or at least that's how I experienced it), it's pretty great here. I took the train from San Jose to SFO once: there was only one train every hour or so, which took something like 2:30 hours at a snails pace to get to San Francisco, then I had to get on the BART (which is actually pretty good), then I needed to get on the AirTrain, all just to get to the departures. By car it usually takes less than an hour... There really is no excuse for that...
The US doesn't have great train systems for the most part but, as you say, in the region that's most comparable to much of Western Europe, the Northeast, it really isn't all that different.
ADDED: What you tend not to have in the US is compact walkable towns and small cities once you get out of the large cities. Though I'd also say, that at least in the UK, small towns away from the main railroad lines will have bus service that's probably better than the US equivalent but it may still just be a few times a day.