UK national railway is sort of free market. The state runs the network, sells the tickets and decides the routes, but provides are chosen in open tenders - lowest price wins. They get paid for operating the route for the state-owned network.
But it then usually turns out that the only operator who can bid on the new tender for the route is the existing one. After all, they have a ready supply of trains meeting the technical spec! And if, say, the drivers go on strike demanding yet another pay rise, the providers shrug their arms and ask the state for a top up. After all, the state doesn't have an alternative either.
Free markets lead to maximizing corporate profits, but it's not a given that these correlate to a positive outcome for the society.