I've never had a need for my AAdvantage card. For ticketing, you're in the computer by name. You need an ID. If you want miles, you can just give them your FF number and they can look it up. If you need partner lounge access based on status, your status should be printed on your boarding pass.

The only time I've had to show my AAdvantage card in recent memory was to get the free snack/drink as an EXP sitting in Y, but the FAs have been pretty good at looking at the manifest these days so I haven't needed it.