Airline deregulation was a huge controversy in the US back a couple of decades. The way in which the full cost/full service airlines keep going bust every 5 minutes might seem to support the contention that it was a bad idea. Similarly in the EU, with Alitalia, Air France and such receiving subsidies, Swissair going bust etc. Both markets have also seen the rise of the budget airlines, Southwest, JetBlue, Easy,  RyanAir. Of course I would argue that the changes were beneficial, consumers have greater choice at lower prices, exactly those things that we expect free markets to deliver.
However, here’s a little snippet that shows just what was wrong with the old system, part of which survives:

The UK’s three biggest airlines, British Airways, Virgin and bmi, are this week set for a fierce battle for the right to operate extra flights to India, one of the most lucrative routes in aviation.
The Civil Aviation Authority will allocate a further 21 direct flights per week to India on Thursday. BA currently owns the rights to all 19 flights a week, which are typically sold out months in advance.

International routes (ie non intra US and non intra EU) are still governed by the old rules of rights to fly allocated by a bureaucracy. There are a few "open skies" agreements but the default condition is that permission must be sought before one is allowed to operate a flight between countries. This isn’t talking about safety and such, that’s dealt with separately. Time for this system to go. The low prices and freedom to travel that competition have brought within the two major markets need to be extended to the global market.