I have a lot of experience taking trains all over Europe. In almost no case was a train cheaper than flying once I included transportation to the airport. The few times a train costs more the difference is marginal and you'd end up flying Ryanair or Easyjet --- no thanks.
> And then the profitability of short distance routes is a direct product of the density of population.
Not a problem in the Northeast in the US. Only Amtrak can fail to offer a service that works everywhere else in the world.
That said, I don't understand the hate for easyJet. It's one of my favourite airlines, being straightforward, well-informing, and no more crammed than your usual cattle class option in a traditional airline.
In this case it wasn't that the trains were more or less expensive, but they were just slow from point A to B. I think Americans have a romantic notion that trains are great all over Europe, but it really does depend on the country. Western Europe, with Italy and Germany in particular seem to have a great high speed rail system. Eastern Europe has trains, but they are not nearly as efficient time wise.
You can only book train tickets three months in advance in Germany.
That said, currently they seem to reach only to mid-December so I don't really know.
And then the profitability of short distance routes is a direct product of the density of population.
This would look differently if airlines were charged for the CO2 externalities (i.e. not receive a de facto subsidy). But we all know how's the carbon pricing going in America ...