The basic problem is that the market does a poor job of accounting for externalities, so indirect costs (pollution, subsidies) are dumped across whole populations over a long period, thus becoming effectively invisible, while profits are scrupulously accounted for and distributed to a far smaller group of recipients.

No. It is externalities not properly being accounted for in the cost.

> Train prices are prohibitively high

They didn't need to be, the problem is that Deutsche Bahn is expected to be profitable since two decades (as a result of the failed attempts to privatize it) - and that includes the cost of physical infrastructure, which is enormous.

An airport however is cheap to build (okay, jokes like the BER aside) and operate, not to mention subsidies for regional airports whereas the EU has been pushing for de-subsidizing and liberalization of the railways for decades now.

Sometimes those 29€ are just the emerged part if the iceberg, with local airports subsidies which distorts said market.

If you look at this article[0], the subsidies can be 100€ per passenger [0] https://www.lechotouristique.com/article/il-y-a-trop-d-aerop... (french)