The Admirals Club and an aircraft cabin are not public areas. AA has rules and regs for both. Granted, the gate area and airport are public. Some of the ACs have quiet areas. LAX and ORD come to mind. IIRC ORD even has a glassed off room where cell phones are not allowed. So it is an issue for enough people to prompt AA to create cell free zones. I have noise cancelling headphones but don't typically wear them unless I plan on listening to something. I guess I will stick to the cell free areas until I find my apartment in Japan
