The problem with this is the airlines have a long history of self destructive behavior. Given the opportunity, they will cut corners at virtually every opportunity - from crew qualifications to maintenance. Left to their own designs, they will eventually destroy themselves by creating a situation where flying is no longer as safe as it currently is, demand will drop, and the industry will collapse. The problem with allowing this to occur is once the damage is done, it will take years (and undoubtedly encounter a great deal of resistance) to fix.

The analogy I'd draw would be the habitat destruction caused by overpopulation of a species, for example snow geese - an excerpt from the Audobon society:

...the geese will spread across much of the Arctic, devastating huge areas of tundra, and then millions of them will suffer malnourishment, disease, and starvation, leading to a population crash. But by that time, they will have destroyed the habitat for many other species. Studies show that once degraded, this habitat will take decades, at least, to recover.

While I am very much a capitalist/free market guy, I can't think of any evidence that airlines will manage themselves responsibly given completely free reign. I believe a healthy balance of power (tension) between management, labor, and appropriate regulation creates a stronger and more stable industry.