What we have now is one of the ridiculous "private non-market" arrangements. When airlines in Europe fly empty planes to stop the government from taking their flight slots away, that's not the fault of the companies, but it's also not a functional market we should expect efficiencies from.
I'm not a fan of "regulate markets into dysfunction then nationalize them", but if the fundamental restraints on travel are too severe to let the market function freely, privatization stops making much sense.