Deregulation has been tough on the airline industry, especially labor. However, I believe that the problem lies more with the bankruptcy process and the courts than the free market.
Labor has been rendered impotent by the complexity of the RLA along with the bias of the mediators. There is no reason any labor group should have to negotiate for more than a year for a new contract without being released to self help. Look at ASA for a good present day example of being completely powerless in the negotiation process.
The BK laws in this country have allowed inefficient companies to survive, thus bloating the market with too much supply and supporting their idiotic pricing schemes. If a business plan doesn't work, companies just take their losses out of the pockets of employees, creditors, and taxpayers.
The courts have also set a dangerous precedent by forbidding labor groups to withdraw their services after the imposition of wages and work rules by the company. Where are employees supposed to turn? The court allows the company to impose whatever conditions they like and labor has no power to object.
If we were truly deregulated, there would be fewer players in the game, but they would be profitable. The weaker, less efficient airlines would liquidate or be consolidated into stronger companies, reducing supply, making all others stronger and more able to set a fair price for travel. In regulation, the government propped up the airlines. Today, through BK and an unfair negotiating process, labor and creditors serve the same function.