AA not only identifies status based on phone number (or permits one to enter one's AA # if the phone is not registered), but the call is routed accordingly and the agent immediately asks whether one is calling about the next itinerary. If not, a simple request for the PRN and that is pulled up.
The reality is that many of the problems are caused by poor IT which requires passengers to call to accomplish tasks which should be handled online. There will always be people who choose to call, but that number dwindles every year. The less routine the call centers handle, the more time to focus on complex issues.