It is though? Are you gonna open a second unconnected subway system in new York and compete with them? That's always the question for a natural monopoly I thought.

Youre gonna have another company digging a second set of tunnels?

Does it make any sense whatsoever to have two?

Not really. Tokyo has an entirely publicly owned subway system. And a separate subway system that was govt owned and then, after buildout, sold some shares to the public via IPO.

With a fare cap to prevent them from screwing over the public.

Japan is very much an oddball in terms of capitalist nations. They are basically the only highly capitalist nation where corporations still put a high value on delivering high quality services and products at reasonable prices. They haven't yet ran into the vulture capitalist problems every other nation has. There's nothing stopping that from happening other than cultural values AFAIK.

Britain and the US are both good examples where privatization of the rail systems has been a complete mess. The US being the worst public transit rail system of any developed nation.