Let them run the railroad, let others run the trains.
The UK started out with railroads in private ownership. They were nationalized in 1948, as British Rail. Then they were de-nationalized in the 1980s and 1990s. Now, they're being re-nationalized.
None of this is considered a huge success.
You say that the railroad is a business, not a private residence. All right, does Home Depot have to let Lowe's use part of their floor space? No, they don't.
Even if those weren't a thing, there's a coherent political view (which I'm not arguing for) that "resolves" the issue: nationalizing the infrastructure and licensing access back like the UK.
It's a strawman though. There's no reason anyone needs to hold identical political views on the property rights of private houses, home improvement stores, and rail infrastructure. They're different things.
(It's a little different in the case of commuter rail, where there's a contractual arrangement.)
This is the same argument behind having multiple providers to share one set of power lines, telephone cables, etc. Duplicate copies of physical infrastructure are pointless, wasteful, and unlikely to occur in practice, so there’s rarely competitive pressure.