Thats a great post, but the thing is the phrase "we apologize for any inconvenience this may've caused" has a very useful psychological purpose: Diffusion.

Lets assume that I know you are mad, possibly pissed. Possibly so pissed that you are going to move your business away to someone else. By saying "sorry for the inconvenience", I diffuse your feelings....make it sound like "I'm sure you preferred to get there earlier....but no biggie, right?"

By giving you a sincere, heartfelt apology I validate all those reasons of why you are pissed. Gives you justification for your further actions.

Regardless, I don't see why it even matters to AA in this case. Thanks to FAA/Local Airport they have de facto monopolies for certain routes, in reality they don't need to apologize at all. (god, I wish competition existed in air travel).