The market can never provide because it’s too cost-effective

Except that's the exact opposite of the problem with rail. The cost of construction is too high, and if you charged the fare that it would require to recoup those costs in some reasonable amount of time, your ridership would drop, making you need higher fares, etc.

It's not cost effective from the perspective of a private person who builds/owns/operates the railroad. That's why the private sector has such a hard time extracting wealth from it. It only becomes cost effective from a government perspective, since the government would benefit from all economic activity the railroad facilitates.