Most railway systems are publicly owned and that seems to work best in the world we currently live in. Smaller systems, like trams and metros are operated by cities and even smaller ones by groups for the fun of it. It really is not that much of a problem, if you do not exclude people working together in coops, local governments and so forth in a solarpunk future. That will be necessary all over the place. For longer distances you need either lots of smaller systems agreeing on standards or a large one run by a large organization. Both can be made to work.