Furthermore, the company cannot just allow customer reps to 'bend a policy here,
[...] expedite an order there, [...] bubble an issue up to a manager'. If you
give them the freedom to bend policies, they can choose to draw their own lines
and that can result in adverse effects for the company overall. Bending of rules
is too risky for a large company to allow their customer reps to take. It's a
slippery slope, but honestly one that doesn't seem to have much of a solution.
That's not true. Zappos, for example, is famous for its excellent customer service. They can, and do give their CS reps a significant amount of autonomy (within guidelines, of course) and allow reps to make on-the-spot calls about sending replacement items or handling refunds. It's a matter of trust and customer focus. Is the company willing to trust the CS rep to make the right call? Is the company focused on doing what's right for the customer and keeping customer loyalty in the long term even when it creates costs in the short term? Both of those things are true for Zappos. I'd suspect that neither of those things are true for American Airlines.
So, why is that? It's not because Zappos is a small company nor is it because American Airlines is a huge one. It has to do with markets. Zappos is in a highly competitive market. Not only are they competing with other online retailers, but they're competing with brick-and-mortar stores as well. In order to sell shoes online, they know that they have to not only match the offline shopping experience, but exceed it, in order to make up for the inherent risk premium assigned to novel types of shopping. They edge they've chosen is customer service. Zappos has the generous return policy that it has because they know that you're already sacrificing some convenience in shopping with them. They know that it's easier to buy (and return) shoes at a brick-and-mortar store, so they want to remove as many other obstacles as they can.
American Airlines, on the other hand, is not in a competitive market. They've split the market with Delta, United, and Continental. They don't have to care about the customer. They know that as long as they're not significantly more or less terrible than the other three carriers, the average consumer isn't going to stick to his or her principles at the cost of a less convenient or more expensive flight. In addition, the airline business has sufficiently high barriers to entry that they don't have to worry about a competitor springing up and devouring their business overnight. That's the real reason American Airlines doesn't care about its customers. It's also the same reason that, e.g. Comcast and Verizon don't have great customer service either. Simply put, they're not forced to, so they don't.