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Most of the Japan railway system was built by the state and privatized later.

Building it isn't the difficult part, keeping it running efficiently is. See: Britain.

Not too sure what you're getting at, but the only part of Britain's rail network that runs acceptably is TFL which isn't privatised.

Ironically most of the railways in Britain were built independently by private companies then nationalised then privatised again.

So what? what is expensive on a daily basis is maintenance and operations. That's the killer.