It has certainly been a success with respect to making flying affordable for the American public. It has certainly not been a success with respect to lending any kind of stability to the industry.
Airlines have never been companies operated around efficiency (SouthWest being the only real anomaly), which was fine when the industry was regulated, as airline A didn't have to compete against airline B (at least on price). This promised profitability to all, however, it also promised to keep air travel something only the relatively wealthy could afford. This situation did, however, have the nice side benefit of making airline employees well compensated, as there was plenty of money to spread around beyond the shareholders and management.
I think the real problem with the current system is twofold. One, the fact that the majority of the Legacy carriers are still big, fat, dinosaur companies that only make decisions when they are forced to, and do so in a very reactionary nature. None of them seem able to look further ahead than 3 months. This does not lend itself to efficient operation.
However, the larger problem is that, in most industries when a competitor puts you out of business (by having a superior product and/or by being a better run company), you are out of the game. The natural business cycle will weed out the losers, and the winners will be left to compete against each other. This environment fosters efficiency, and the end consumer benefits. Ever notice that when you go purchase a new cooling fan for your computer, you have the choice of only 3 companies? The 4th company- who's fans either failed too soon, had excessive warranty claims, or were not priced to compete in the market- is no longer in business.
The whole concept of government bailouts is the biggest problem, in my opinion. It gives little incentive to any company to succeed, knowing that if they don't, they'll be given a second chance. And in this case, third, fourth, etc. Furthermore, the ability to shed debt and financial obligations during a restructuring allows the loser competitors to come back to the table for a second round, with an advantage that the remaining companies do not have. And thus this cycle continues, until at some point every company has been on both the "winners" and "losers" list.
The above cycle burns tax payer money, and, while it benefits consumers at face level with low fares, hurts the economy in the long run. In my opinion, it should either be a government run industry (which would include all the problems any government agency has, but allow stability) or let it float as a free market, which will decide the winners and losers once and for all.