The hole is very deep. There's no way out that isn't slow and painful.
This article looks promising, but then think about the disaster that is the private ISP industry or the red-light camera industry in the US. The US is bad at privatization, we tend to turn it into exploitative subsidies of crony capitalists. http://marketurbanism.com/2010/12/22/japanese-transit-and-wh...
Edit: found the underlying case, [2], but it looks less than straightforward -- the fixed fair was a condition of the leases on the right-of-way of the train system, and the attempt was made to charge a second fare when a certain boundary was crossed.
[1] https://books.google.com/books?id=LYSVd43vZwQC&lpg=PR13&ots=...
[2] https://supreme.justia.com/cases/federal/us/279/159/case.htm...