That railway example is just a plain market failure, and an uncorrectable one at that. Markets only work under certain conditions, very important among those: absence of monopoly, monopsony and limitations that work to the same effects. A privatized rail network is still the only rail network in the country or region, so still a monopoly. If you hack it to bits and split it up too much, it will be useless, connectivity is paramount in that business. If you leave it as a large network (or several large networks) it will be a national or regional monopoly. Having only the government pay is a monopsony. Limiting building new stations and tracks (which the government will have to do at some point, if real estate prices don't) will also prevent competition. So having a functioning rail market is impossible, therefore any argument about market mechanisms involving railways (or roads, water, gas and electricity distribution) is nonsense: Those can never be proper free markets.
