Over here Ben Southwood makes a case against nationalizing the British train lines:
Returning it to centralised state control would be a step backwards and a mistake.
Instead we should end the practice of franchising, which creates private monopolies, and allow real competition and diversity.
The solution to our current problems is not more state bungling, it is a return to diversity, competition and open markets.
Are there (modern) examples here nations have adopted a true free market approach to the railways, which includes "real competition and diversity"? Most nations that I'm familiar with have some sort of private railway, but no real competition/free market since on most lines you can "choose" just one company (which is exactly the situation in the UK).
If such examples exist, how do these systems work? (e.g. one of the problems with organising a true open market is that you can't run two trains on the same track at once).